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In this paper, the energy-to-peak filtering problem for the uncertain discrete-time singular bilinear systems is studied. This paper considers the uncertainties that consist of real systems and the possible data packet dropouts when performance output signals and measurement output signals are transmitted over digital channels. In the course of the study, the phenomenon is elucidated utilising the Bernoulli random binomial distribution. The goal is to design the desired filter, so that the filtering error system is admissible, and meets the specified energy-to-peak performance index. The design conditions of energy-to-peak filters for uncertain discrete-time singular bilinear systems are given by introducing the Lyapunov function and using linear matrix inequalities (LMIs). The impact of uncertainty on singular bilinear systems is addressed using a two-step approach. At last, a numerical illustration is provided to demonstrate the validity of the design. [ABSTRACT FROM AUTHOR]

This work presents a contribution to reduce the conservatism in nonlinear observer for TakagiSugeno fuzzy systems with unmeasurable premise variables based on the mean value theorem. The conservatism was reduced through the use of non-quadratic Lyapunov function (NQLF) rather than the quadratic form used in previous works. The stability conditions are given in the form of Bilinear Matrix Inequalities (BMI) whereby an effective solution to solve this type of problem is presented using linear solvers which are characterized by their computational efficiency. To show the improvement of the proposed work over the existing approach and to demonstrate its effectiveness in solving the Bilinear Matrix Inequalities, the feasibility area is illustrated by a numerical example, and a real-time implementation of the observer is applied to the induction motor (IM) where a big number of inequalities is present. • Using the TS fuzzy model representation which obtained by using the non linear sector transformation. • Reducing the conservatism of the classical Mean Value Theorem observer by using the polyquadratic Lyapunov function. • Presenting an iterative linear matrix inequalities method to solve bilinear matrix inequalities using linear optimization solvers. • Real-time implementation of the proposed observer on an induction motor. [ABSTRACT FROM AUTHOR]

This article is to investigate the consensus control and initialization region optimization for leader‐following multi‐agent systems with time‐varying communication delay and nonidentical consecutive packet dropouts. By combining the Bernoulli distribution model of the data loss and the Hadamard product, the control protocols affected by both communication delay and packet dropouts are utilized to formulate the consensus problem into the mean‐square stability problem of the augmented error systems. Resorting to the Lyapunov function methodology and a structure separation method, a sufficient condition to ensure the consensus is built in the form of linear matrix inequality. Relying on the given Lyapunov function and set‐membership analysis, an optimization procedure is proposed to simultaneously ensure the consensus and enlarge the estimated ellipsoid of initial conditions. The validity of the provided method is illustrated through a comparative simulation. [ABSTRACT FROM AUTHOR]

This paper investigates a networked control system with bounded and time‐varying delays. Also, an observer‐based predictive controller is developed for the active compensation of the network communication delay since it may lead to poor performances or even unstable dynamics for the systems. The existence of the state observer can be established by choosing an appropriate Lyapunov function, and to do this, Luenberger observer gain is computed with Linear Matrix Inequality (LMI) based on the stability conditions of the system. The practical aspect of this research, different from previous works, is the accessibility of the states that are not always available for the system. Controller and observer gains and other essential variables are derived through LMI. In the closed‐loop system, which is modeled as a switching system, the switches are based on communication delays. Using the Lyapunov stability method for switching systems, sufficient LMI conditions are derived to guarantee the stability of the closed‐loop system. Finally, the results of the simulation have demonstrated the performance of the methodology presented. [ABSTRACT FROM AUTHOR]

ABSTRACT In this article, the reachable set estimation problems for a class of singular discrete‐time nonlinear systems (SDNS) with time‐varying delay (TVD) are presented. First, we employ a Lyapunov function scheme and utilize zero‐type free matrix equations. Based on this, a criterion is derived in the form of linear matrix inequalities (LMIs) to guarantee that the considered system to be regular, causal, and the state trajectory x1$$ {x}_1 $$ of the system is bounded. Second, by developing the singular systems decomposition technique into slow and fast subsystems and using the introduced auxiliary lemma, we establish that the x2$$ {x}_2 $$ state trajectory of the fast subsystem is also bounded, and the reachable set of singular nonlinear system is bounded within the ellipsoid. Finally, Numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates the robust secure output tracking control for a class of uncertain two‐dimensional (2‐D) networked control systems. The 2‐D systems are described by the well‐known Fornasini–Marchesini (FM) local state‐space model, the parameter uncertainties are assumed to reside in a polytopic region, and the deception attacks are supposed to occur randomly in the transmission process. In the problem formulation, Bernoulli random variables are used to characterize the phenomena of deception attacks. As main results, a novel H∞$$ {H}_{\infty } $$ performance analysis condition for the augmented closed‐loop system is proposed by using a novel parameter‐dependent Lyapunov function and some zero equalities. Furthermore, both parameter‐dependent and parameter‐independent controllers have been designed, respectively, such that the output of the 2‐D systems tracks the output of a given reference model well in the H∞$$ {H}_{\infty } $$ sense. The design conditions are presented in terms of linear matrix inequalities (LMIs). In the end, a numerical simulation on a practical thermal process is applied to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT This article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed. [ABSTRACT FROM AUTHOR]

ABSTRACT In this article, new linear matrix inequality (LMI) conditions are proposed to guarantee robust stability of the closed‐loop of the linear time‐invariant one‐dimensional uncertain system by dealing with both continuous‐time (CT) and discrete‐time (DT) cases. These improved conditions for robust state feedback control combine the non‐monotonic approach and Finsler's technique. The benefit of the non‐monotonic approach returns to the utility of an arbitrary number of quadratic functions by considering the higher order derivatives of the vector field in the CT case (or the higher order differences of the vector field in the DT case). Finsler's technique aims to solve the closed‐loop stability problem in a larger parametric space. The strong points of the suggested LMI conditions are easy to program, eliminate the product between the state matrix and Lyapunov matrices, reduce the constraints by avoiding the decrease monotonically along trajectories for each quadratic Lyapunov function, guarantee the robust stability of the closed‐loop by using a state‐feedback gain. The simulation results show and confirm the effectiveness of these proposed conditions. [ABSTRACT FROM AUTHOR]

This article considers exponential stabilization (ES) of switched interval type‐2 (SIT2) fuzzy systems with asynchronous switching control. The SIT2 fuzzy system switches from one mode to another according to transition probabilities (TPs). A general SIT2 fuzzy quantized event‐triggered output controller (QETOC) is designed to save the communication resources. The QETOC employs distinctive membership functions from those of the IT2 fuzzy model and switches with mode‐pendent switching delay, which is more practical than asynchronously switched control techniques with a common switching delay and control schemes without TP. By designing discretized multiple Lyapunov function (DMLF) and using convex combination technique, sufficient conditions formulated by linear matrix inequalities (LMIs) are obtained to ensure that the DMLF does not 'jump high' at the moment of switching, and hence the conservatism of obtained results is significantly reduced since no additional dwell time is needed for the stabilization. It is discovered that the SIT2 fuzzy system is not necessary to be unstable on mismatched intervals, and it can be unstable on matched intervals. The advantages of theoretical analysis are verified by numerical simulations, and the classical assumption that each subsystem is unstable on mismatched intervals is conservative for control design. [ABSTRACT FROM AUTHOR]

This paper investigates the state and actuator fault reconstruction problem in a class of switched linear systems subjected to unknown external disturbances according to average dwell time (ADT) technique. First, a robust switched sliding mode observer (SMO) is developed to simultaneously reconstruct the states of the switched system and the actuator faults. A novel and less conservative sufficient stability conditions are then established using the multiple quadratic Lyapunov function technique and the ADT approach. These conditions are formulated as linear matrix inequalities (LMI) to facilitate the design of the SMO. The observer gains matrices are obtained throughout the resolution of LMI using convex optimization techniques. Next, actuator faults are estimated by utilizing the concept of equivalent output injection, achieved through an analysis of the state error dynamics during the sliding motion. Finally, simulation results are considered to illustrate the applicability and efficiency of the developed method. It showcases the rapid and accurate convergence of the estimated system states and actuator fault to the real variables. [ABSTRACT FROM AUTHOR]

In this paper, we present a characterization of diagonal solutions for a class of linear matrix inequalities. We consider linear hybrid time-delay systems and explore the conditions under which these systems are positive and asymptotically stable. Specifically, we investigate the existence of positive diagonal solutions for a linear inequality when the system matrices are Metzler and nonnegative. Using various mathematical tools, including the Schur complement and separation theorems, we derive necessary and sufficient conditions for the stability of these systems. Our results extend existing stability criteria and provide new insights into the stability analysis of positive time-delay systems. [ABSTRACT FROM AUTHOR]

In this manuscript, it is investigated that the stability property of a discrete-time switched system consisting of all unstable subsystems. Under a switching signal with certain conditions, the sufficient constraints for asymptotic stability of a discrete-time switched system composed of all unstable subsystems are obtained via Lyapunov functions and the defined divergence time. Furthermore, based on this result, linear matrix inequalities are obtained for asymptotic stability of a linear discrete-time switched system composed of all unstable subsystems. The efficiency of the acquired theorems is exhibited by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a new method for regional stabilization of discrete-time nonlinear systems by static output feedback based on polynomial Lyapunov functions. The considered class of nonlinear systems subject to time-varying parameters can be described by difference-algebraic representation and an equivalent polytopic model is obtained, making it possible to apply Lyapunov theory and linear matrix inequality-based tool. In this sense, a convex optimization problem in terms of LMI is provided to guarantee the closed-loop system's robust stabilization and to enlarge the estimated domain of attraction (DoA). The proposed control design is a one-step approach that can be applied to systems with nonlinear output matrices. It requires no iterative algorithms or congruence transformation, and auxiliary decision variables are introduced only aiming at less conservative results. Besides that, the use of polynomial Lyapunov functions allows us to obtain asymmetric and non-convex estimated DoA, reducing the conservativeness. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This article considers a path tracking control problem for autonomous vehicles constrained to maintain a safe distance from the next vehicle in the lane. The control design problem is solved by considering a mathematical model of the vehicle that jointly describes the lateral and longitudinal dynamics. Specifically, the ℒ2$$ {\mathcal{L}}_2 $$ optimal controller is designed aimed at minimizing the orientation and position tracking errors with respect to a given reference path. Moreover, the controller is able to ensure that the vehicle can both follow a speed profile and automatically adjusts the vehicle speed to maintain a proper distance from the next vehicle. The lateral dynamic is regulated by a 2‐DOF feedforward/feedback controller, where the feedforward law is implemented by exploiting an inverse kinematic model of the vehicle. On the other side, the feedback action, along with the action of the controller in charge to regulate the longitudinal dynamics, is the ℒ2$$ {\mathcal{L}}_2 $$ optimal gain‐scheduling state‐feedback controller. In particular, a parameter‐dependent quadratic Lyapunov function approach is used to reduce the conservativeness of the solution and a suitable convex LMI optimization problem is formulated for the synthesis. The vehicle is described by a seven‐degrees‐of‐freedom (7DOF) full‐car model, with the tire‐generated forces described by the classical Pacejka's Magic Formula. In order to assess the performance of the proposed control strategy, simulations have been undertaken in Matlab/Simulink by considering an autonomous vehicle driving into an urban scenario. [ABSTRACT FROM AUTHOR]

The issues of state estimations based on distributed observers for linear time-invariant (LTI) systems with multiple sensors are discussed in this paper. We deal with the scenario when the information exchange has known time delays, and aim at designing a distributed observer for each subsystem such that each distributed observer can estimate the system state asymptotically by rejecting the time delay. To begin with, by rewriting the target system in a connecting form, a subsystem which is affected by the time-delay states of other nodes is established. And then, for this subsystem, a distributed observer with time delay is constructed. Moreover, an equivalent state transformation is made for the observer error dynamic system based on the observable canonic decomposition theorem. Further, in order to ensure that the distributed observer error dynamic system is asymptotically stable even if there exists a time delay, a linear matrix inequality (LMI) which is relative to the Laplace matrix is elaborately set up, and a special Lyapunov function candidate based on the LMI is considered. Next, based on the Lyapunov function and Lyapunov stability theory, we prove that the error dynamic system of the distributed observer is asymptotically stable, and the observer gain is determined by a feasible solution of the LMI. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time boundedness problem of switched linear systems under periodically intermittent control. Sufficient conditions are established to guarantee finite-time boundedness or finite-time stability of switched linear systems under periodically intermittent control. The proof procedures are implemented successfully resorting to piecewise Lyapunov functions. Based on the linear matrix inequality technique, the conditions are casted into a convex optimisation problem and therefore, they can be efficiently handled. The method proposed in this paper is a much potentially useful one in practice because of its economical and efficient nature that is easy to employ. Finally, two examples are given to express the validity and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, model predictive control (MPC) was considered for a class of discrete time-delay systems with external disturbances. Equivalent input disturbance (EID) is a commonly utilized active disturbance rejection technique that enhances the rejection of system disturbances. Any disturbance can be effectively suppressed using the EID approach, leaving no traces of the disturbance. This paper proposes a novel MPC control approach that combines the EID method with the MPC principle. An MPC law with disturbance-rejection performance was presented after obtaining and combining the EID estimates with performance indicators using the EID method. Optimizing the performance index is then converted into a semi-definite problem comprising of an objective function and linear matrix inequality through building a Lyapunov function. Based on this basis, an MPC design algorithm is proposed. A numerical simulation was conducted to confirm superiority and efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the practical asymptotic stabilization of a desired equilibrium point in discrete-time switched affine systems. The main purpose is to design a state feedback switching rule for the discrete-time switched affine systems whose parameters can be extracted with less computational complexities. In this regard, using switched Lyapunov functions, a new set of suffcient conditions based on matrix inequalities, are developed to solve the practical stabilization problem. For any size of the switched affine system, the derived matrix inequalities contain only one bilinear term as a multiplication of a positive scalar and a positive definite matrix. It is shown that the practical stabilization problem can be solved via a few convex optimization problems, including Linear Matrix Inequalities (LMIs) through gridding of a scalar variable interval between zero and one. The numerical experiments on an academic example and a DC-DC buck-boost converter, as well as comparative studies with the existing works, prove the satisfactory operation of the proposed method in achieving better performances and more tractable numerical solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a decoupled unknown input observer (DUIO) for Takagi-Sugeno (T-S) systems, designed specifically for the synchronous reluctance motor (SynRM). The proposed DUIO method demonstrates enhanced robustness and accuracy in state estimation by effectively decoupling the influence of unknown inputs from the estimation error dynamics. Furthermore, the DUIO exhibits superior performance compared to the proportional integral observer (PIO) and the proportional multi-integral observer (PMIO) presented in previous studies, without the need for prior knowledge of the unknown input form or assumptions regarding its boundedness. Stability conditions, achieved using the quadratic Lyapunov function, are expressed as linear matrix inequalities (LMIs), which ensure asymptotic convergence of the estimation error. The effectiveness of the DUIO method is further validated in various scenarios through hardware-in-the-loop (HIL) implementation. This innovative approach significantly enhances the accuracy and reliability of SynRM state estimations and unknown input detections. [ABSTRACT FROM AUTHOR]

This study focuses on bumpless transfer (BT) fault detection in switched linear systems operating under mode‐dependent average dwell time (MDADT) switching. We propose a piecewise fault detection filter (FDF) inspired by the segmentation concept inherent in the multiple discontinuous Lyapunov function (MDLF) approach. This filter generates a residual signal that effectively minimizes the amplitude of residual bumps, surpassing the performance of traditional non‐piecewise FDFs. We introduce a new definition of residual BT performance, aimed at reducing residual bump amplitude during filter transitions. The goal is to design the piecewise FDF such that the augmented system maintains asymptotic stability with weighted H∞$$ {H}_{\infty } $$ performance, while also meeting the residual BT performance criteria. The feasibility of achieving H∞$$ {H}_{\infty } $$ BT fault detection filtering is established through linear matrix inequalities (LMIs), leveraging the MDLF and MDADT strategies. The efficacy and benefits of the proposed BT piecewise FDF design are demonstrated through simulations on a boost converter. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-triggered control of switched two-dimensional (2D) continuous-discrete systems in Roesser model. A more general event-triggered scheme is proposed to reduce unnecessary resource waste and data redundancy, where a weighing coefficient and multiple parameter matrices are used. Based on the proposed event-triggered mechanism, a state feedback controller and a state-dependent switching signal are proposed. By using the multiple Lyapunov function method, sufficient conditions for the exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, two examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper examines a nonlinear Networked Control System (NCS) incorporating Takagi–Sugeno (T–S) fuzzy models to address the output tracking control problem in the presence of input state delay. The paper introduces a strategy based on an event-triggered scheme to reduce bandwidth utilization in the NCS by leveraging inherent constraints, including communication time delays and data transmission limitations. The presence of communication time delay leads to an asynchronous interaction between the designed control algorithm for T–S fuzzy systems, which utilizes novel LMI–based conditions, and the proposed T–S fuzzy controller. Additionally, this paper proposes a model of operation based on synchronous behaviour, enabling the design of a linear controller that is more easily implementable. In comparison to recent literature results, these results are obtained by using an associate Lyapunov Krasovskii Function (LKF) with fuzzy properties, in addition to different forms of integral inequalities as alternatives. A fuzzy model for NCSs is illustrated through an example of tracking control for output response. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust decentralized control of discrete-time nonlinear interconnected descriptor systems (IDS) under the influence of external disturbances. First, we utilize the Takagi–Sugeno fuzzy model (TSFM) to represent discrete-time nonlinear IDS. For controller design, a proportional-derivative (PD) feedback strategy is employed to formulate a decentralized fuzzy controller for the discrete-time Takagi–Sugeno IDS (DTTSIDS). Furthermore, robust and passivity constraints are incorporated into the controller design process to mitigate the effects of disturbances. Based on the Lyapunov function and free weight function methods, we can analyze the stability of the DTTSIDS. The proposed conditions are converted into Linear Matrix Inequality (LMI) conditions through Schur Complement technology so that we can solve the problem through MATLAB LMI-Toolbox. Finally, the effectiveness of the proposed methodology is demonstrated through three examples presented in the paper and a comparison with other existing studies is given in Example 3. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor. [ABSTRACT FROM AUTHOR]

This paper deals with the fault detection observer (FDO) design for discrete-time switched singular systems (SSSs) under persistent dwell time (PDT) switching. Compared to the widely used dwell time and average dwell time switching in the literature, PDT switching is more general due to its covering such two switchings as special cases. The PDT switching is firstly employed to establish the admissibility criterion and the H ∞ and H - observer synthesis conditions for SSSs. Also, an efficient H - / H ∞ FDO design algorithm is proposed. First, the admissibility analysis of the observing error system is addressed by incorporating the PDT technique into the multiple Lyapunov function method, and an admissibility criterion in the form of linear matrix inequality is established. Based on this, two FDO synthesis conditions are then developed to guarantee that the generated residual signal achieves prescribed H ∞ and H - performance with regard to disturbances and faults, respectively. The FDO should be designed such that the effects of faults and disturbances on the residual signal are maximized and minimized, respectively. To this end, the FDO design is expressed as a multi-objective optimization problem, and the FDO gains are characterized in terms of the solution of the multi-objective optimization problem. Moreover, a suitable trade-off between the robustness to disturbances and the sensitivity to faults is obtained based on a corresponding proposed algorithm. Finally, one illustrative example is given to show the validity of the developed method. [ABSTRACT FROM AUTHOR]

In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $ H_{\infty } $ H ∞ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $ H_{\infty } $ H ∞ . The scheme's effectiveness is demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

The time-varying delay is a peculiar phenomenon that occurs in almost all systems. It can cause numerous problems and instability during system operation. In this paper, the time-varying delay is considered in both the states and input vectors, which is a significant distinction between the proposed method here and previous algorithms. Furthermore, the time-varying delay is unknown but bounded. To address this issue, the Razumikhin approach is applied to the proposed method, as it incorporates a Lyapunov function with the original non-augmented state space of the system models, in contrast to the Krasovskii formula. Moreover, the Razumikhin method performs better and avoids the inherent complexity of the Krasovskii method, particularly when dealing with large delays and disturbances. For achieving output stabilization, the model predictive control (MPC) is designed for the system. The considered system in this paper is an interval type-2 (IT2) fuzzy T-S model, which provides a more accurate estimation of the dynamic model of the system. The online optimization problems are solved using linear matrix inequalities (LMIs), which reduces the computational burden and online computational costs compared to offline and non-LMI approaches. Finally, an example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In stabilization of a Large-Scale System (LSS), the decentralized nature of the controller is a significant issue, because centralized controllers are difficult and impractical for real-time implementation. The designing procedure for decentralized controllers should guarantee the stability of the overall LSS and at the same time, allow limited information exchange in the LSS. In this paper, a decentralized controller for a nonlinear LSS modeled by a Linear Parameter Varying (LPV) model is designed. The controller design procedure is formulated as a convex feasibility problem which can be solved by finding a feasible answer to some Linear Matrix Inequalities (LMIs). The solution to this feasibility problem assures a fully decentralized controller where information exchange among local controllers is forbidden and, only data transfer among each controller and its corresponding subsystem is allowed. In the proposed approach, the Lyapunov function of the LSS equipped with local controllers is considered as the sum of the Lyapunov functions of all subsystems. Then, the stability conditions are derived to assure the stability of the LSS. After designing a decentralized controller to ensure LSS stability, the same approach is exploited for H ∞ and H 2 performance improvement of the LSS in the presence of disturbances. To verify the efficacy of the designed controller, a large-scale power system which is a practical example is considered, and the proposed approach is applied on it. The simulation results prove the appropriateness of the designed local controllers. • A decentralized controller is designed for a large-scale linear parameter varying system. • A fully decentralized controller with limited information exchange among subsystems is designed. • The controller is designed in three cases; stabilization, H ∞ and H 2 performance improvement. • The stabilization design procedure is formulated as a convex feasibility problem. • The H ∞ and H 2 design procedures are formulated as convex optimization problems. [ABSTRACT FROM AUTHOR]

This paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies. [ABSTRACT FROM AUTHOR]

This note puts forward continuous event‐triggered impulsive control (CETIC) and dynamic event‐triggered impulsive control (DETIC) to discuss a class of (integral) input‐to‐state stability (iISS, ISS) for nonlinear systems (NSs), where the impulse sequences are produced by certain predesigned event‐triggering conditions. Different from traditionary event‐triggered control (ETC), CETIC indicates that a controller will be stimulated only if the given state‐dependent event condition is invoked. There exist no transfer of control between two continuous impulse triggered instants. Compared with the traditional static ETC, the DETIC can efficaciously lessen controller update and dramatically save energy at the same decay rate. In addition, all sample path solutions (SPS) for the system have the lowest time between events guaranteed to be positive. Utilizing CETIC strategy, we get some Lyapunov conditions to effectually avoid infinite triggering behavior and obtain the ISS‐type stability of the investigative systems. Then, one applies the theoretical consequences to NSs and derive a class of ETC mechanism with impulsive control gains (ICG) by linear matrix inequalities (LMIs). Because of the existence of timer, the DETIC strategy naturally excludes Zeno phenomena. Furthermore, conclusions in this thesis permit the upper bound estimation for the differential Lyapunov function coefficient to be time‐varying function instead of a constant in certain extant results, which means the criteria of the Lyapunov technique in this paper is less conservative and looser. Eventually, three examples with related simulations are demonstrated to indicate the rationalization and usefulness of our conclusion. [ABSTRACT FROM AUTHOR]

• Proposed a new switched epidemic model arising from changes in contact rates in an infected society. • Considering vulnerable individuals as vaccination frontiers along with the possibility of vaccine failure. • Qualitative analysis of the model using two theorems on positive invariance set and positivity of solutions. • Global stability analysis of equilibria, with a focus on the basic reproduction number (R 0) as a bifurcation value. • Manipulating the contact rates between subsystems through the contact-rate-dependent average dwell time to control a disease. This paper introduces a switched SQWVEAIR (Susceptible, Quarantined, Weak, Vaccinated, Exposed, Asymptomatic, Infected, and Recovered) epidemic model considering changing contact rates in an infected society. It also takes into account the presence of vulnerable individuals as frontiers in vaccination, recognizing their societal importance. The qualitative analysis of the model involves two theorems on the positive invariance set and the positivity of the solutions. Additionally, it calculates the equilibria of the proposed model and analyzes their global stabilities using the Lyapunov functional technique, focusing on the basic reproduction number (R 0) as a bifurcation value. To achieve globally uniformly exponential stability, it calculates the contact-rate-dependent average dwell time (CRDADT) for each stable and unstable subsystem, developing a Lyapunov function. It also derives sufficient conditions, expressed as linear matrix inequalities (LMIs), to ensure stability. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and validate our research findings. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example. [ABSTRACT FROM AUTHOR]

The main focus of this article is to explore the finite‐time stabilization of time‐varying cyber‐physical systems (CPS) that are operating over multipath networks and under random denial‐of‐service (DoS) attacks. In contrast to prior studies, we present a set of necessary and sufficient conditions for achieving finite‐time stability in the closed‐loop model of CPS operating over single‐path network. Notably, this equivalent conditions are established based on the analysis of the state transition matrix (STM). Additionally, we utilized auxiliary systems to study more general CPS operating over multipath networks and obtained a sufficient condition based on STM. Finally, we address a sufficient condition based on the Lyapunov function and introduce a linear matrix inequality (LMI)‐based approach that facilitates the computation of nonfragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

For the nonlinear parameter‐varying (NPV) model of unmanned surface vehicle with the consideration of the velocities on yaw and surge as well as wave disturbances, a robust H∞$$ {H}_{\infty } $$ control method is proposed based on extended homogeneous polynomial Lyapunov function (EHPLF) to regulate heading for the superior performance on the rapidity, accuracy, and robustness. First, a NPV model of heading error is established to design a general form of a state feedback controller with a robust H∞$$ {H}_{\infty } $$ performance. Second, a Lyapunov matrix with full states and varying parameter is constructed to derive the robust H∞$$ {H}_{\infty } $$ global exponential stability conditions by Euler's homogeneity relation for the NPV system, known as the EHPLF stability conditions. Third, since the EHPLF stability conditions consist of a set of nonlinear coupled inequalities that cannot be directly solved by sum of squares (SOS) toolboxes, they are decoupled with matrix transformations to obtain the EHPLF‐SOS stability conditions, which is solved for the parameters of the state feedback controller. Finally, the simulation results indicate that EHPLF method exhibits a superior performance on dynamic, steady‐state, and robustness. [ABSTRACT FROM AUTHOR]

Currently, output-feedback control still necessitates severe constraints on systems, e.g., system nonlinearities cannot exceed certain degree and uncertainties should belong to specific types. In this paper, by exploiting dynamic-compensation mechanisms, we essentially extend system nonlinearities and uncertainties. Specifically, the nonlinearities heavily rely on unmeasured states and particularly have unknown arbitrary function-of-output growth rates. Unknown control coefficients whether with known or unknown bounds are admitted, which have been excluded before in the context of such inclusive nonlinearities. The key to our novel solution lies in realizing the potential of filter-based observers, dynamic high gains, design/analysis parameter designation, and composite Lyapunov functions. In detail, two dynamic-high-gain filters are worked out to provide available states for controller design. The filter states, after weighted by the unknown control coefficient, also make up the estimated states which lead to control-free and tractable error dynamics. Two dynamic high gains with new dynamics are put forward to counteract the nonlinearities and uncertainties and, meanwhile, to enable the adaptive controller to own a concise structure. During the controller design, crucial design parameters can no longer be expressed explicitly due to unknown control coefficients, but rather need to be pursued through a recursive algorithm. With a set of analysis parameters, important (dynamic-high-gain) input-to-state stable properties of some vital variables are uncovered, and exhaustive Lyapunov analysis is performed for the closed-loop boundedness and convergence. [ABSTRACT FROM AUTHOR]

The paper studies the problem of robust tracking of the fuzzy systems in the presence of uncertainties. A robust feedback controller based on the linear matrix inequality (LMI) is proposed using a Lyapunov function combined with the supervisory controller. Hence, the sufficient stability condition for the general type of robust fuzzy tracking controls has been formulated and the performance of the controller has been tested for different classes of the fuzzy models. It has been demonstrated that the smooth fuzzy compositions have better performance rather than the standard fuzzy compositions, (i.e., min–max compositions and product–sum compositions). Considering that the smooth fuzzy compositions are efficient in face of the uncertainties, it is believed that the present work opens up new doors for wider applications of the smooth fuzzy compositions in the industry. [ABSTRACT FROM AUTHOR]

This paper proposes an observer-based proportional Derivative (O-BPD) fuzzy controller for uncertain discrete-time nonlinear descriptor systems (NDSs). Representing NDSs with the Takagi–Sugeno fuzzy model (T-SFM), the proportional derivative (PD) feedback method can be utilized in the fuzzy controller design via the Parallel Distributed Compensation (PDC) concept, such that the noncausal problem and impulse behavior are avoided. A fuzzy observer is proposed to obtain unmeasured states to fulfill the PD fuzzy controller. Moreover, uncertainties and transient response performances are taken into account for the NDSs. Then, a stability analysis process and corresponding stability conditions are derived from the Lyapunov theory with the robust control method and the pole constraint. Different from existing research, the Singular Value Decomposition (SVD) and the projection lemma are utilized to transfer the stability conditions into the Linear Matrix Inequation (LMI) form. Because of this reason, the conservatism of the analysis process can be reduced by eliminating the restriction on the positive definite matrix in the Lyapunov function. By giving the proper center and radius parameters of the pole constraint in the O-BPD fuzzy controller design process, the expected transient responses can be obtained for different designers and different practical applications. Finally, the effectiveness and applicability of the proposed O-BPD fuzzy controller are demonstrated by two examples of the simulation. [ABSTRACT FROM AUTHOR]

In this study, a new robust predictive control technique is investigated for uncertain fractional-order descriptor systems. Using the properties of fractional calculus and the construction of an appropriate Lyapunov function, the sufficient conditions to guarantee the existence of a robust predictive controller are given by minimizing the worst-case optimization problem. The new robust predictive controller is presented by using Shur complement, linear matrix inequality toolbox and cone-complement linear algorithm, and it is proved that the feasible solution of the optimization problem at the initial time can guarantee the admissibility of fractional-order descriptor closed-loop system. [ABSTRACT FROM AUTHOR]

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The current paper verifies the asynchronous H ∞ control and optimization problem for flight vehicles with a time-varying delay. The nonlinear dynamic model and Jacobian linearization establish the flight vehicle's switched model. An asynchronous H ∞ tracking controller is designed, considering the existing asynchronous switching between the controllers and corresponding subsystems. In order to promote transient efficiency, the tracking controller comprises the model-based part and the learning-based part. The model-based part guarantees stability and prescribed efficiency, and the learning-based part compensates for undesirable uncertainties. The multiple Lyapunov function (MLF) and mode-dependent average dwell time (MDADT) methods are utilized to guarantee stability and the specified attenuation efficiency. The existing conditions and the solutions of model-based sub-controllers are represented by linear matrix inequalities (LMIs). The deep Q learning (DQL) algorithm provides the learning-based part. Different from the conventional method, the controller parameters are scheduled online. Therefore, robustness, stability, and dynamic efficiency can be met simultaneously. A numerical example illustrates the efficiency and advantage of the presented approach. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the problem of fault estimation for a class of continuous‐time switched affine systems with actuator faults. In most of the existing results of switched affine systems based on the min‐switching approach, the candidate Lyapunov function is usually common, such that it is conservative to derive the practical stability conditions. To overcome this restriction, a class of switched Lyapunov function is introduced to increase more degrees of freedom of the designed min‐switching strategy and to ensure the stability of error systems. At the same time, the proposed dwell‐time dependent switching strategy can avoid the frequent switchings commonly existing in the min‐switching mechanism. Then, a new intermediate estimator is designed to estimate the state and fault simultaneously, and the intermediate estimator based fault estimation is performed under the proposed mixed switching law. Moreover, the gains of fault estimator are explicitly calculated via resolving the conditions of linear matrix inequalities. Finally, two examples including a flyback DC‐DC power converter are illustrated to verify the effectiveness and advantage of proposed fault estimation approach. [ABSTRACT FROM AUTHOR]

This paper introduces an H ∞ robust constrained event-triggered fuzzy controller for discrete-time nonlinear systems in the presence of system parameter uncertainties, the parameter uncertainties of the output matrices and the disturbances, simultaneously. To reduce the communication resources and improve the robust performance, the event-triggered mechanism is incorporated with the H ∞ robust fuzzy controller design. Moreover, by employing the fuzzy modeling of the actuator saturation and a nonquadratic Lyapunov function (NQLF), the ultimate bounded stability (UBS) of the closed-loop system is guaranteed subject to the amplitude limitations of the control signal. This means, a new linear matrix inequality (LMI) problem is derived to ensure the robustness and constraints in an offline scheme based on the event-triggered strategy. Besides, to meet the practical problem to further improve the controlled system performance, the control input rate constraint is also considered and a new LMI condition is provided with no online computational burden. Therefore, the computational burden of the proposed controller is greatly reduced with less conservatism. Two simulation examples including a numerical dynamic system and a truck–trailer system are employed to illustrate the less conservatism and computational complexity of the proposed method compared with the existing approaches. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of asynchronous event-triggered guaranteed cost control for two-dimensional Markov jump systems in Roesser model. The hidden Markov model is introduced to characterize the asynchronous phenomenon induced by imperfect mode detection, and a hidden Markov model-based event-triggered mechanism is employed in controller design to reduce the communication burden of the network. By using the quadratic Lyapunov function technique, some sufficient criteria are developed to ensure the asymptotic stability of the addressed system with a guaranteed cost value under three different boundary conditions. Finally, an optimization algorithm with linear matrix inequality constraints is formulated to design the optimal asynchronous event-triggered guaranteed cost control law, and a simulation example is considered to illustrate its validity. [ABSTRACT FROM AUTHOR]

This paper addresses a mode-dependent state-feedback H ∞ control for stochastic descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H ∞ performance γ of the closed-loop system are proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator-saturated control input is expressed as a linear combination of a given state-feedback control input and a virtual control input that always remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the conditions for the existence of both the mode-dependent state-feedback H ∞ control and the ellipsoidal shape invariant sets are successfully derived in terms of LMIs. Two numerical examples demonstrate the effectiveness of the proposed method by solving optimization problems subject to the proposed LMIs that minimize H ∞ performance γ and maximize the invariant set, respectively. [ABSTRACT FROM AUTHOR]

The strategy of observer‐based nonfragile control and fault‐detection over finite‐time horizon has been examined for a class of uncertain switched nonlinear networked control systems (NNCSs) contingent with time varying delays inferred by the networks from sensor to controller and controller to actuator. Also, in this study, an observer‐based fault detection control has been designed for the NNCSs. By making use of fault detection control as residual generator, the conveyed fault detection problem is then transformed into H∞$$ {H}_{\infty } $$ attenuation problem. By employing multiple Lyapunov function and average dwell time (ADT) approach, sufficient conditions in terms of linear matrix inequalities (LMIs) ensures the finite‐time boundedness (FTB) criterion of the resulting switched NNCSs with a prescribed disturbance attenuation. Subsequently, the preferred LMIs constraints realizes the controller and observer gains. Finally, two numerical examples are proffered to showcase the efficacity of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability. [ABSTRACT FROM AUTHOR]