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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]

As a giant in energy consumption, buildings urgently need to optimize control strategies for the main energy consuming equipment inside buildings. It is of great significance to design advanced control algorithms to improve the efficiency of the main energy consuming equipment in buildings, namely air conditioning, in the current energy shortage. The model predictive control algorithms and strategies were used in this study to control the HVAC system to improve the energy utilization of the city. Then linear matrix inequality with robust model predictive feedback controller was used to optimize and get the model predictive control optimization algorithm. The research results showed that, under the influence of different factors, the three regions controlled by the model predictive control optimization algorithm showed a little overshooting in the initial state. But it was quickly corrected after adjustment. Meanwhile, the average tracking error of temperature and humidity in each region was 0.139°C and 0.13g/kg dry air, respectively. The average predicted mean vote was 0.32. In actual office buildings, the proposed algorithm controlled the temperature within the reference value range of 0.1°C throughout the entire process. The total electricity consumption and electricity price costs were reduced by 12.11% and 22.54%, respectively. In summary, the proposed method has good performance for HVAC system application, which can effectively realize energy saving and emission reduction and improve human comfort. This method makes important contributions to promote the construction of smart cities and the development of green buildings. [ABSTRACT FROM AUTHOR]

This article addresses the problem of designing an event‐triggered fault detector within a networked nonlinear system described by a Takagi–Sugeno (T–S) fuzzy model, accounting for time‐varying delays and denial‐of‐service (DoS) attacks characterized by a binary Markov chain. Our focus is on constructing an event‐triggered residual system, which aims to detect malfunctions in the original fuzzy system while optimizing communication resource allocation. Specifically, it is tailored to combat DoS attacks in the event generator‐to‐fault detector channel and mitigate network‐induced time‐varying delays. Utilizing the Lyapunov–Krasovskii function approach, we formulate linear matrix inequalities to establish the necessary conditions ensuring the asymptotic mean‐square stability of the residual system, meeting a predefined H∞$$ {H}_{\infty } $$ performance criterion. Finally, the simulation results are presented to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the ϖ (t) , which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method is introduced through using the variable impulsive gain and time-varying delays. It is interesting to find that uncertain time-delay systems can maintain GES by adjusting the impulsive gain and impulsive delay. Finally, two simulations are given to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This article is dedicated to event‐triggered anti‐disturbance control of networked control systems via a guaranteed cost triggering scheme. A distribution interconnected observer structure is built to estimate these unknown matched disturbances. A novel event triggered condition is constructed in terms of real‐time cost and averaged functions composed of observer states and the last successfully transmitted one. A composite control scheme is provided by an event‐triggered observer‐based state feedback controller and compensators for the matched disturbances. A sufficient condition in term of linear matrix inequality is supplied to ensure the asymptotic stability of the resultant closed‐loop system. A simulation is carried out to demonstrate the effectiveness of the proposed triggering control strategy. [ABSTRACT FROM AUTHOR]

This paper presents the decentralized sampled‐data fuzzy observer design technique for nonlinear interconnected systems based on the Takagi–Sugeno fuzzy model. The interconnected system is considered that the subsystems include uncertain interconnections and are not needed to satisfy stable conditions. Based on the continuous‐time Lyapunov functional approach, the observer design technique is proposed to minimize the interconnection bound to attenuation degree ratio and formulated into the linear matrix inequality formats. Finally, by simulation example, it shows the validity and superiority of the proposed observer design technique. [ABSTRACT FROM AUTHOR]

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature. [ABSTRACT FROM AUTHOR]

This article focuses on the finite‐time mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passive filtering problem for discrete‐time singular systems with randomly occurring nonlinear perturbations. The main purpose is to design a filter, which ensures the singular error system is stochastically finite‐time bounded and satisfies mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passive performance. By constructing an augmented matrix, the properties of matrix determinant and rank are used to prove that the singular system is regular and causal, Finsler's lemma and Projection lemma are used in the design process to acquire additional slack variable matrices, thereby enhancing the solution space with extra degrees of freedom. Then, the unknown parameters of the filter are obtained by solving the less conservative linear matrix inequalities. Finally, the feasibility of the proposed method is verified through a common numerical example and by controlling a DC motor for an inverted pendulum. [ABSTRACT FROM AUTHOR]

• Memory sampled-data control is applied for the uncertain rigid spacecraft model. • Randomly missing measurement in the system output obeys the Bernoulli distribution. • It tolerates uncertainty and disturbances using the H ∞ technique. • A novel looped and delay-dependent LKF is constructed for the proposed systems. • It gives the minimum disturbance attenuation level compared with existing works. This paper focuses on stabilizing the attitude of the rigid spacecraft under the sampled-data control design technique with constant communication delay. The system dynamics with model uncertainty (perturbation) and missing measurements are considered. The aim is to design a desirable attitude control that ensures the stabilization of the rigid spacecraft with an optimal H ∞ performance level. A novel Lyapunov–Krasovskii functional is developed, incorporating looped characteristics, for the proposed study on the rigid spacecraft model by developing relevant new terms. Making use of the Lyapunov function as well as free-matrix-based integral inequality, sufficient stability criteria are established to assure the stability of the rigid spacecraft model. Furthermore, the desired sampled-data control gain matrices are acquired through the solution of linear matrix inequalities, which guarantees the asymptotic stability of the rigid spacecraft model. Finally, the numerical simulation demonstrates the efficacy of the theoretical study proposed for the rigid spacecraft model. [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]

Present paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately. [ABSTRACT FROM AUTHOR]

This article investigates the output feedback H∞$$ {H}_{\infty } $$ control problem of linear systems with infinite distributed input delays. An observer‐based output feedback (OBOF) H∞$$ {H}_{\infty } $$ controller is proposed via the predictor feedback approach, and a sufficient condition for the existence of the OBOF H∞$$ {H}_{\infty } $$ controller is given in terms of a set of linear matrix inequalities. It is shown that the resulting closed‐loop system is globally exponentially stable with a prescribed H∞$$ {H}_{\infty } $$ performance. The obtained results include some results on the same problem for linear systems with bounded distributed input delays as special cases. Two numerical examples are finally presented to illustrate the effectiveness of the proposed H∞$$ {H}_{\infty } $$ controller. [ABSTRACT FROM AUTHOR]

This work proposes a design methodology for predictive control applied to the single-phase PWM inverter with an LC filter. In the design, we considered that the PWM inverter has parametric uncertainties in the filter inductance and output load resistance. The control system purpose is to track a sinusoidal signal at the inverter output. The designed control system with an embedded integrator uses the principle of receding horizon control, which underpinned predictive control. The methodology was described by linear matrix inequalities, which can be solved efficiently using convex programming techniques, and the optimal solution is obtained. MATLAB-Simulink and real-time FPGA-in-the-loop simulations illustrate the viability of the proposed control system. The LMI-based MPC reveals an effective performance for tracking of a sinusoidal reference signal and disturbance rejection of input voltage and load perturbations for the inverter subject to uncertainties. [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 is concerned with the problem of asynchronous finite‐time dynamic output feedback (DOF) control for a class of discrete‐time switched linear systems under the admissible edge‐dependent average dwell time (AED‐ADT) switching scheme. The main goal of the paper is to design a DOF controller to ensure that the resulting closed‐loop system is finite‐time bounded with AED‐ADT switching and has a specific H∞$$ {H}_{\infty } $$ performance. Firstly, some new sufficient conditions for stability criterion and H∞$$ {H}_{\infty } $$ performance analysis are established based on the multiple Lyapunov functionals technique and the linear matrix inequalities method. Secondly, a type of DOF controllers that guarantee that the closed‐loop system has desired performance is designed. Finally, the effectiveness of the proposed approaches is elaborated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur'e system with the application of fractal interpolation based image encryption. The variable-order fractional Lur'e system is modeled into fractional order Chua's circuit model with short memory. The synchronization is achieved using event-triggered impulsive control and short memory for chaotic Lur'e systems, employing linear matrix inequalities. The variable-order fractional Chua's circuit systems successfully accomplish their synchronization using both impulsive and event-triggered impulsive control. Furthermore, fractal interpolation function (with function scalings) is applied to reconstruct the chaotic attractors. The Riemann-Liouville variable-order fractional calculus of diverse fractal functions is also investigated in connection with the study on variable-order fractional systems. The interpolated sequence, along with the Arnold transform, modified Fisher Yates algorithm, and additive diffusion, is utilized to propose an image encryption algorithm. Various statistical analyses are conducted to assess the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the mean-square bounded consensus issue in a two-layer multi-agent network under deception attacks. The two-layer network is composed of the leader and follower layers with a switching topology. Employing an impulsive control method, the mean-square bounded consensus for the leader layer and the node-to-node mean-square bounded consensus of the two-layer network are analyzed. Based on the knowledge of graph theory, Lyapunov stability theory, and linear matrix inequalities, sufficient conditions for the mean-square bounded consensus of multi-agent systems in the two-layer network are derived. Finally, the practicability and efficacy of the theoretical outcomes are corroborated via the provided numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, the guaranteed cost control problem for a class of nonlinear networked control systems (NCSs) with dynamic quantization, external bounded disturbance, and data dropout is investigated via the dynamic output feedback. The Takagi–Sugeno (T-S) fuzzy model is used to represent the discrete-time nonlinear system discussed in this paper. Under the dynamic quantization strategy, two quantizers with dynamic parameters are used to quantize the measured output and control input, and the data dropout process is described by introducing the Bernoulli stochastic variable. By using the quadratic boundedness technique, the quadratic stability of the quantized NCS with external disturbance is described. Furthermore, the sufficient condition for the global design approach are proposed, that is, not only the dynamic output feedback controller but parameters of the quantizers are designed synchronously with strict linear matrix inequalities. Eventually, a simulation of nonlinear mass-spring-damper mechanical system is carried out to verify the effectiveness of the provided algorithm. [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]

The paper addresses the switching-like event-triggered control for uncertain networked control systems with time-varying delay under DoS attacks. First of all, to reduce the communication burden, a switching-like event-triggered mechanism is designed to automatically select the trigger condition according to whether the system is under DoS attacks, which have the advantage of reducing the number of data packets transmitted. Secondly, unlike the traditional assumption of time-varying delay, here it satisfies the condition that the probability is known, and combines the networked control systems to propose a novel time-delay system model, which can obtain a larger upper bound on the delay. Then, by using both the Lyapunov functional method and linear matrix inequality technique, we obtain sufficient conditions of uncertain networked control systems to achieve exponentially stable in the mean square sense. Furthermore, under the common limitations of the maximum continuous packet losses caused by the DoS attacks and delay, the stability criterion is derived, which can be used to estimate the communication parameters and security controller gain. Finally, through two simulation examples, the larger upper bound of time delay, less trigger times, faster convergence rate are obtained, which verify the validity of our theoretical analysis. • An event-triggered mechanism is designed which can switch the trigger threshold. • A new delay model based on Bernoulli distribution is introduced. • Lyapunov function method and linear matrix inequality techniques are used. • The uncertain networked control systems remain robust exponentially stable in the mean square sense under DoS attacks. [ABSTRACT FROM AUTHOR]

This paper presents an observer-based dynamic output-feedback controller design procedure using linear matrix inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state-feedback gains, and observer gains are coupled into a dynamic output-feedback optimal controller. The LMI set used in the two stages is matrix inversion free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of non-fragile H∞ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed H∞ performance level γ. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified. [ABSTRACT FROM AUTHOR]

In this article, the problem of the optimal reset control design for Lipschitz nonlinear systems is addressed. The reset controller includes a base linear controller and a reset law that enforces resets to the controller states. The reset law design is strongly dependent on the appropriate design of the base controller. For this reason, in this article, the base controller and reset law are simultaneously designed. More precisely, an optimal dynamic output feedback is considered as the base controller which minimizes the upper bound of a quadratic performance index, and a reset law is used to improve the transient response of the closed‐loop system. This design is done in a full offline procedure. The problem is transformed into a set of linear matrix inequalities (LMIs), and the reset controller is obtained by solving an offline LMI optimization problem. Finally, two examples are presented to illustrate the effectiveness and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Sensors are a key component in industrial automation systems. A fault or malfunction in sensors may degrade control system performance. An engineering system model is usually disturbed by input uncertainties, which brings a challenge for monitoring, diagnosis, and control. In this study, a novel estimation technique, called adaptive unknown-input observer, is proposed to simultaneously reconstruct sensor faults as well as system states. Specifically, the unknown input observer is used to decouple partial disturbances, the un-decoupled disturbances are attenuated by the optimization using linear matrix inequalities, and the adaptive technique is explored to track sensor faults. As a result, a robust reconstruction of the sensor fault as well as system states is then achieved. Furthermore, the proposed robustly adaptive fault reconstruction technique is extended to Lipschitz nonlinear systems subjected to sensor faults and unknown input uncertainties. Finally, the effectiveness of the algorithms is demonstrated using an aircraft system model and robotic arm and comparison studies. [ABSTRACT FROM AUTHOR]

The structured singular value (SSV), or μ$$ \mu $$, is used to assess the robust stability and performance of an uncertain linear time‐invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full‐blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full‐blocks. This specific class of uncertainty is relevant for the input‐output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full‐blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full‐blocks. The upper bound can be formulated as a semi‐definite program (SDP), which we solve using a standard interior‐point method to compute optimal scaling matrices associated with the repeated full‐blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full‐block structure. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fault detection in DC microgrids in the presence of denial-of-service (DoS) attacks. To deal with the nonlinear term in DC microgrids, a Takagi-Sugeno (T-S) model is employed. In contrast to the conventional approach of utilizing current sampling data in the traditional event-triggered mechanism (ETM), a novel integrated ETM employs historical information from measured data. This innovative strategy mitigates the generation of additional triggering packets resulting from random perturbations, thus reducing redundant transmission data. Under the assumption of faults occurring within a finite-frequency domain, a resilient event-based H − / H ∞ fault detection filter (FDF) is designed to withstand DoS attacks. The exponential stability conditions are derived in the form of linear matrix inequalities to ensure the performance of fault detected systems. Finally, the simulation results are presented, demonstrating that the designed FDF effectively detects finite-frequency faults in time even under DoS attacks. Furthermore, the FDF exhibits superior fault detection sensitivity compared to the conventional H ∞ method, thus confirming the efficacy of the proposed approach. Additionally, it is observed that a trade-off exists between fault detection performance and the data releasing rate (DRR). [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]

Summary: With the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed H∞$$ {H}_{\infty } $$ and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights. [ABSTRACT FROM AUTHOR]

The focus of this article is to present a sawtooth-characteristic-based free-matrix integral inequality and to discuss its application to sampled-data systems (SDSs). Firstly, the free matrix, which is associated with the sawtooth characteristic of the input delay, is presented and incorporated into the integral inequality. In the development of inequality techniques, this is the first time that a free matrix has been associated with the sawtooth characteristic. On this basis, a corresponding sawtooth-characteristic-based free-matrix integral inequality is established, enabling estimation of the integral quadratic terms of the Lyapunov–Krasovskii functional (LKF) derivative. To overcome the challenges posed by second-order terms resulting from the proposed integral inequality, augmented system variables associated with the sawtooth characteristic are also introduced. Thus, the complicated calculation arising from second-order terms and the conservatism caused by the quadratic estimation of the LKF can be avoided. Finally, through the utilization of the sawtooth-characteristic-based free-matrix integral inequality, stability criteria with less conservatism are derived for the SDSs in the form of linear matrix inequalities. The superiority of the proposed approach is illustrated through two numerical examples and a simplified sampled-data based power market. • A sawtooth-characteristic-based free-matrix integral inequality is proposed for the first time. The novelty of this inequality technique is that the commonly used constant free matrix is set to be input delay, i.e., d k 1 (t) -dependent matrix. This is the first time that a free matrix has been associated with the sawtooth characteristic. • Some augmented system variables associated with the input delay d k 1 (t) and the corresponding free-weighting-matrix are introduced to reduce the high-order terms of d k 1 (t). Thanks to the introduction of augmented system variables, the complicated calculation arising from d k 1 (t) 2 -related terms as well as the conservatism caused by the quadratic estimation of the LKF, can be avoided. Meanwhile, some high-order LKF that have been abandoned by scholars because of cumbersome calculations can also be selected as LKF candidates without quadratic treatment. • The proposed sawtooth-characteristic-based free-matrix integral inequality is employed for sampled-data system. The integral quadratic terms of the LKF derivative can be converted into some sawtooth-characteristic-dependent terms by the proposed integral inequality, and less conservative stability criteria for SDSs are obtained. [ABSTRACT FROM AUTHOR]

This article discusses the finite‐time mixed H∞$$ {H}_{\infty } $$ and passive filtering design problem for uncertain nonlinear singular systems. The parameter uncertainties are constrained by well‐defined upper bounds on their magnitudes. The objective is to design a full‐order filter to ensure that the augmented singular system to be finite‐time boundedness(FTB) with H∞$$ {H}_{\infty } $$ and passivity performance. Firstly, a sufficient condition for achieving singular finite‐time boundedness with mixed H∞$$ {H}_{\infty } $$ and passivity performance for uncertain nonlinear singular system is derived by introducing a free matrix. Secondly, a novel criterion is established for analyzing finite‐time H∞$$ {H}_{\infty } $$ and passivity problem of filtering error singular system based on augmented matrix technique. Thirdly, the filtering design conditions are presented and the relevant parameters of the desired filter are determined using linear matrix inequality decoupling principle. Finally, a practical circuit system and a numerical example are provided to demonstrate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This study presents novel formulations for ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust state‐feedback control synthesis for discrete‐time linear time‐invariant systems based on linear matrix inequalities. The proposed formulations require searching for two adjustment matrices. The synthesis formulations include other formulations from the literature as particular cases according to specific values of the adjustment matrices. We propose the application of evolutionary optimization to determine the optimal values of these two adjustment matrices. One approach to obtaining a single‐step formulation for static output‐feedback control synthesis is to transform a state‐feedback control synthesis formulation via the simple change of variables. The alteration of variables considered in this study requires an adjustment matrix. The adjustment matrix influences the performance of the resulting controller or the existence of a feasible solution to the problem. Here, we also propose the application of evolutionary optimization to determine the optimal value of this adjustment matrix and the two adjustment matrices of the proposed formulations to obtain the optimal ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust control system. Case studies verify that despite the increased complexity, the proposed formulations and the method required to tune them may be indispensable in achieving a robustly stable control system or an enhanced ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance for more intricate problems. [ABSTRACT FROM AUTHOR]

The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is studied. First, like a normal system, the whole nonlinear system is transformed into a local linear system, and then a large number of linear system theories can be applied to solve related problems. Second, in the observer design of general discrete-time Markov jump systems, only the unknown input in the state equation is usually considered. In this paper, the unknown input is considered in both the state equation and the output equation. The state estimation error system is derived by defining the error. The non-uniform Lyapunov functional is selected to stabilize the estimation error system using the Lyapunov theory. The sufficient conditions for the stability of the system are obtained and transformed into the feasibility problem of linear matrix inequality. The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is solved using MATLAB software. Finally, a numerical example of two rules and two modes is used to verify the effectiveness and feasibility of the proposed unknown input observer. [ABSTRACT FROM AUTHOR]

This paper presents a fault detection and isolation (FDI) method applied to a wind turbine system. The approach utilizes a nonlinear sliding mode observer (SMO) to effectively reconstruct faults in both the hydraulic pitch actuator and generator torque actuator of the wind turbine. A Linear Matrix Inequality (LMI) optimization approach is employed for the design. The blade pitch angle and generator torque in the wind turbine have significantly different orders of magnitudes, rendering them vulnerable to faults of different magnitudes. This discrepancy poses a challenge for the simultaneous reconstruction of faults. To resolve this challenge, a modification is made to the observer. To examine the effectiveness of the modified SMO, two fault scenarios were considered for the hydraulic pitch actuator and generator torque actuator. In the first case, faults are introduced separately, while in the second case, faults occur simultaneously. Simulation results demonstrate accurate detection, isolation, and reconstruction of these faults, whether in the case of separate or simultaneous fault occurrences. [ABSTRACT FROM AUTHOR]

In this work, we consider a new class of generalized fractional linear multidimensional state–space systems described by the Roesser model. We discuss a novel technique for analysing robust stability, focusing specifically on the stability of the closed-loop system in terms of the $ \mathcal {H}_2 $ H 2 and $ \mathcal {H}_\infty $ H ∞ norms. Both discrete-time and continuous-time cases are addressed across various regions of the complex plane. An extension of the bounded real lemma is proposed, dealing with both continuous and discrete cases. This lemma is used to provide sufficient conditions, in the form of linear matrix inequalities, to ensure stability margin for the perturbed system. Motivating examples are presented to demonstrate the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

This paper studies a secure iterative interval estimation approach for cyber-physical systems subject to stealthy deception attacks. Under the hypothesis that the system is accessed by a stealthy attack, an iteration scheme integrating the T-N-L observer framework is employed to reconstruct the system state. With the help of a structure separation method, a sufficient condition in terms of linear matrix inequality is provided to obtain convergent observation errors under deception attacks. Resorting to the reachability analysis, a secure state interval is built by means of the analyzed attack bounds and the observation error interval. Simulation studies verify the effectiveness of the proposed method for attack and attack-free cases. [ABSTRACT FROM AUTHOR]

This paper proposes a Modified model reference adaptive controller and observer (MMRACO) for unknown linear time‐invariant (LTI) systems. The recent literature, and in particular the so‐called MRACO approach, has demonstrated how some deficiencies in standard model reference adaptive control can be overcome by using a combination of modified reference models and observers, but this is done at the expense of knowing bounds on certain unknown parameters. Here, a novel adaptive observer/controller combination is presented which removes the need to know the above bounds but preserves the other desirable features of the MRACO approach. A Lyapunov analysis of the closed‐loop system ensures asymptotic convergence of both tracking and observer errors, with uniform boundedness of parameter estimation errors. A key advantage of the scheme is that the design involves only solutions of two Lyapunov equations (or linear matrix inequalities) and does not require the selection of a "high gain" parameter. The effectiveness of the approach is illustrated in some numerical examples. [ABSTRACT FROM AUTHOR]

This article addresses the issue of event‐triggered security control for nonlinear cyber‐physical systems, characterized by Denial‐of‐Service (DoS) attacks, time‐varying delays, and actuator faults. These complexities are captured using the Takagi–Sugeno fuzzy model. Significantly, this study focuses on DoS attacks targeting the controller‐to‐actuator channel, and subsequently introduces a model for actuator faults that considers the prolonged utilization or degradation of component parts. To optimize communication resource allocation, a model‐independent event‐triggered mechanism is proposed. Utilizing the Lyapunov–Krasovskii function approach, the objective of achieving stochastic stability is transformed into a linear matrix inequalities problem, thus deriving a set of sufficient conditions. The efficiency and validity of the proposed algorithms is demonstrated through simulation results. [ABSTRACT FROM AUTHOR]

In the set-point following, the asymptotic property of the stability would disappear in the presence of time-varying references and disturbances. Hence, the boundedness of state variables is an essential issue in the regulation. To this aim, in light of time-varying references and disturbed signals, a robust integral policy is systematically developed to achieve the control aim in the uncertain equations with delay. Utilizing linear matrix inequality, a guideline is suggested for guaranteeing the boundedness of the solutions in uncertain systems with delays. Then, the gains of the control law are computed from a minimization. Although the boundedness is ultimately obtained in the perturbed case, the asymptotic stability would also be deduced for the nominal systems. The findings are numerically evaluated in some simulations. The favorability of the proposed integral method is shown in comparison to the traditional control strategies. • A robust integral scheme is designed considering varying references and disturbances. • The boundedness is guaranteed in the regulation of the uncertain delayed systems. • An LMI-based condition is suggested for the boundedness of all variables. • In the perturbed case, UB is obtained while the asymptotic stability is deduced for the nominal systems. • The superiority of the controller is shown in comparison to the recent control techniques. [ABSTRACT FROM AUTHOR]

This study aims to propose a sampled-data control technique, utilizing a linear matrix inequality (LMI) approach, to achieve string-stable vehicle platooning in a cooperative adaptive cruise control (CACC) system with communication delays. To do this, a decentralized sampled-data controller design technique that combines one controller using sensor measurements and another one utilizing vehicle-to-vehicle (V2V) communication, ensuring both individual and string stability, is proposed first. Next, a memory sampled-data control (MSC) approach is presented to account for transmission delays in V2V communication. Additionally, an improved Lyapunov–Krasovskii functional (LKF) is presented to improve computational complexity and sampling performance. The design conditions are formulated as linear matrix inequalities (LMIs) in the time domain, facilitating efficient stability analysis and optimization. Finally, vehicle platooning simulations are provided to validate the effectiveness and feasibility of the proposed technique. [ABSTRACT FROM AUTHOR]

This study explores the development of H∞$$ {H}_{\infty } $$ dynamic observer (HDO) for discrete‐time nonlinear systems (DTNLS) with time‐varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen‐based inequality (JBI) and the Wirtinger‐based inequality (WBI). These lead to less conservative time‐dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper addresses the robust normalization and stabilization problems for descriptor fractional-order systems with polytopic uncertainties in all system coefficient matrices, including the state derivative coefficient matrix. Firstly, novel sufficient conditions for the robust normality and stability of polytopic uncertain descriptor fractional-order systems are presented based on linear matrix inequalities. Then, for the cases when the uncertain parameters are known and unknown, the proportional and derivative state feedback control with constant feedback gain and parameter-dependent feedback gain are introduced to normalize and stabilize such systems, respectively. Finally, numerical examples are provided to show that the proposed approach is effective and less conservative than the results obtained by other researchers. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a new class of SOS-convex (sum of squares convex) polynomial optimization problems with spectrahedral uncertainty data in both the objective and constraints. By using robust optimization and a weighted-sum scalarization methodology, we first present the relationship between robust solutions of this uncertain SOS-convex polynomial optimization problem and that of its corresponding scalar optimization problem. Then, by using a normal cone constraint qualification condition, we establish necessary and sufficient optimality conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem based on scaled diagonally dominant sums of squares conditions and linear matrix inequalities. Moreover, we introduce a semidefinite programming relaxation problem of its weighted-sum scalar optimization problem, and show that robust weakly efficient solutions of the uncertain SOS-convex polynomial optimization problem can be found by solving the corresponding semidefinite programming relaxation problem. [ABSTRACT FROM AUTHOR]

In this paper, a linear matrix inequality (LMI)-based robust model predictive speed control (RMPSC) with a disturbance observer (DOB) is proposed to guarantee stability and control performance against the parameter uncertainty and disturbance of a permanent magnetic synchronous motor (PMSM). All external torques applied to the PMSM are defined as disturbance, estimated by the DOB, and used to construct the RMPSC method. The proposed DOB and RMPSC are determined by a multiple LMI-based optimization approach. Furthermore, parameter uncertainty within a certain range, due to manufacturing errors or aging deterioration, is considered and a systematic tuning method is proposed to obtain the optimal gains. Finally, an offline optimization method is developed that ensures a low computational load to enable real-time processing. Simulation results demonstrate the effectiveness and validity of the proposed control method. [ABSTRACT FROM AUTHOR]

This work addresses the problem of synchronizing pathological changes in a patient with coronary artery obstruction to the corresponding nominal coronary artery system (CAS) model. The CAS model is characterized by nonlinear terms, so the synchronization problem is transformed into an equivalent time-varying delay T-S fuzzy framework using the sector of nonlinearity approach. New bilinear matrix inequalities (BMIs) conditions for robust stability analysis and dynamic output feedback gain synthesis are derived based on a less conservative condition for stability assessment of T-S fuzzy systems. A simple change of coordinate is used to solve the cross terms of the bilinearities, allowing the problem to be formulated in terms of linear matrix inequalities (LMIs) and solved using standard semi-definite programming. The effectiveness of the controller design approach is demonstrated through extensive simulations under diverse performance criterion that the controller can achieve. [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]

This article is devoted to estimating simultaneously both the states and the inputs of linear time-invariant fractional-order systems (LTI-FOSs) with the order 0 < α < 2 . Firstly, a necessary and sufficient stability criterion for LTI-FOSs with the order 0 < α < 1 is derived by the linear matrix inequality technique. Secondly, a novel fractional-order observer combined with state vectors and ancillary vectors is given, which can generalize several forms of existing observers. Moreover, the parameter matrices of the desired observer for both the order 0 < α < 1 and 1 < α < 2 are solved on the basis of the stability theorem and the solution to the generalized inverse matrix. Finally, the fractional-order observer design algorithm is proposed and then applied to an illustrated example, in which the simulation results are reported to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all defining linear matrix inequalities, and on the cone of positive semidefinite matrices. Here we use results on isometries between matrix algebras to describe linear matrix inequality definitions of relatively small size. We conversely use the theory of operator systems to characterize special such isometries. [ABSTRACT FROM AUTHOR]