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In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an interval multiobserver is designed for nonlinear systems subject to unknown but bounded disturbances and measurement noises. The behavior of discrete nonlinear systems is described by an uncoupled multimodel. Linear Matrix Inequalities (LMIs) are formulated to study the stability of the proposed systems and to ensure the cooperativity dynamic of the observation errors. An augmented system is introduced to apply a tracking control where the control gains are obtained by pole placement. Finally, a numerical example is proposed to verify the efficiency of the interval multiobserver in state estimation and to prove the performance of the control strategy to follow the desired trajectory. [ABSTRACT FROM AUTHOR]

Addressed in this paper is the reachable set estimation (RSE) problem for fuzzy‐model‐based leader‐follower multi‐agent systems with time‐varying delays and false data injection attacks. First, the aperiodic sampled‐data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov‐Krasovskii functional is constructed with the knowledge of sampling patterns and time‐varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the H∞$H_\infty$ performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single‐link robot arm models are employed to validate the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the robust stability and stabilization problems of continuous‐discrete fractional‐order two‐dimensional Fornasini–Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional‐order α∈(0,2)$$ \alpha \in \left(0,2\right) $$, the unified LMI‐based stability conditions are presented by general description of stable root‐clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI‐based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI‐based conditions. Thirdly, facing interval uncertainties in this model, the LMI‐based robust stability conditions and LMI/BMI‐based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results. [ABSTRACT FROM AUTHOR]

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation. [ABSTRACT FROM AUTHOR]

Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach. [ABSTRACT FROM AUTHOR]

The purpose of this article is to propose a novel framework employing a looped‐functional approach for the stability analysis of continuous‐time linear systems with asynchronous sampling. In this approach, a negative forward‐difference of a Lyapunov functional consisting of a Lyapunov function and a looped‐functional sufficiently guarantees asymptotic stability of the sampled‐data systems. To reduce the conservatism of the stability criteria, we develop a consecutive time‐intervals‐dependent looped‐functional approach that satisfies a convex looping inequality with respect to each sampling interval. Compared to the existing looped‐functional approaches, the proposed method provides a more general looped‐functional and in turn a more relaxed stability conditions. The existing looped functionals and their associated looping conditions can be considered as special cases of the proposed ones. This relationship can easily be verified by excluding time‐intervals‐dependent terms in the general looped functional. Four numerical examples that consider both periodic and asynchronous sampling cases demonstrate that the proposed looped‐functional approach shows better performance in terms of allowable maximum sampling intervals at a cost of a small additional number of decision variables. [ABSTRACT FROM AUTHOR]

The simultaneous fault detection and control (SFDC) has emerged as a reliable scheme. However, what happens when the designed structure undergoes changes? Such variations have the potential to cause instability and misdiagnosis. This paper delves into a cutting-edge SFDC structure that surpasses conventional designs in terms of reliability. The proposed Resilient Simultaneous Fault Detection and Control (RSFDC) structure considers variations in the designed parameters and provides a more robust and fault-tolerant approach to SFDC, with important implications for the design of reliable and resilient control systems in a broad range of applications. This scheme is formulated as a multi-objective optimisation problem, encompassing control and diagnosis objectives. Specifically, it aims to minimise the impact of faults and disturbances on the controlled output while reducing residual sensitivity to all changes and maximising the fault effects on the residual. Through simulation comparisons, this paper showcases the merits of the RSFDC structure in two examples, highlighting its superiority over other designs. [ABSTRACT FROM AUTHOR]

In this paper, a class of linear discrete-time systems with input saturation is studied in a data-driven framework. Firstly, the input-state data are collected to represent the open-loop and closed-loop systems. While the open-loop data-based representation is a result that is parallel to system identification, the closed-loop representation bypasses the system identification and can be used for direct data-driven control law synthesis. Then, by a novel Lyapunov technique, sufficient conditions for system stability are derived, such conditions are independent of system matrices. Moreover, the attraction domain is estimated using two classes of shape reference sets. Finally, two examples are used to test the correctness of the data-driven control laws. [ABSTRACT FROM AUTHOR]

Induction motors (IMs) are widely used in industrial applications, but harmonic distortion in IM drives can lead to inefficiencies and reduced lifespan. Traditional control strategies and filtering methods have limitations in mitigating lower-order harmonics, particularly the 5th harmonic, which can generate reverse torque and increase overheating risk. Existing solutions often struggle to fully address these issues, especially in high-power applications with dynamic loading conditions. This paper proposes a control strategy to reduce voltage and current harmonics in a Z-source inverter (ZSI)-fed IM drive. The system incorporates an observer-based output feedback robust servomechanism controller, designed using Linear Quadratic Regulator (LQR) and Linear Matrix Inequality (LMI) techniques. It ensures closed-loop stability, precise tracking regulation, and effective disturbance rejection, while also featuring a speed adaptation mechanism for sensorless operation. Simulation results demonstrate significant harmonic mitigation, with the controller achieving 1.01% lower voltage THD and 1.03% lower current THD compared to conventional approaches. This improvement aligns with industry standards and outperforms several existing techniques. The proposed method contributes a comprehensive solution for harmonic mitigation in high-power IM drives, applicable to various industrial applications requiring high-quality power and precise speed control. [ABSTRACT FROM AUTHOR]

An heterogeneous vehicle platoon controller for autonomous vehicles is proposed in this paper. The traction force of each vehicle is controlled according to the state of the predecessor vehicle, which can be known by LiDAR/RADAR, and the state of the leader vehicle, which is received by vehicle-to-vehicle (V2V) communication. Platoon string stability is evaluated under Lyapunov and H∞ conditions. An iterative procedure is proposed in order to deal with the non-convexity of the static output feedback control design problem. Simulation results demonstrate that the proposed heterogeneous vehicle platoon controller achieves a good overall performance without compromising the safety of any vehicle. The separation between each follower and its predecessor is kept in appropriate ranges, always close to the desired reference. Furthermore, the transient errors are not amplificated when propagated downstream the platoon, therefore string stability is assured. [ABSTRACT FROM AUTHOR]

This paper presents an altitude and attitude control system for a newly designed rocket-type unmanned aerial vehicle (UAV) propelled by a gimbal-based coaxial rotor system (GCRS) enabling thrust vector control (TVC). The GCRS is the only means of actuation available to control the UAV's orientation, and the flight dynamics identify the primary control difficulty as the highly nonlinear and tightly coupled control distribution problem. To address this, the study presents detailed derivations of attitude flight dynamics and a control strategy to track the desired attitude trajectory. First, a Proportional-Integral-Derivative (PID) control algorithm is developed based on the formulation of linear matrix inequality (LMI) to ensure robust stability and performance. Second, an optimization algorithm using the Levenberg–Marquardt (LM) method is introduced to solve the nonlinear inverse mapping problem between the control law and the actual actuator outputs, addressing the nonlinear coupled control input distribution problem of the GCRS. In summary, the main contribution is the proposal of a new TVC UAV system based on GCRS. The PID control algorithm and LM algorithm were designed to solve the distribution problem of the actuation model and confirm altitude and attitude tracking missions. Finally, to validate the flight properties of the rocket-type UAV and the performance of the proposed control algorithm, several numerical simulations were conducted. The results indicate that the tightly coupled control input nonlinear inverse problem was successfully solved, and the proposed control algorithm achieved effective attitude stabilization even in the presence of disturbances. • A newly designed thrust vector control based rocket-type UAV prototype is presented. • The governing equations of the under-actuated and unstable dynamics system are derived. • A robust PID controller based on the formulation of LMI guaranteeing robust performance in the sense of the Lyapunov is designed. • A configuration of the GCRS is designed to realize the thrust vector control. • A LM-based optimal algorithm is presented to solve the nonlinear force inverse mapping problem induced by the GCRS. [ABSTRACT FROM AUTHOR]

In this paper, we study the bivariate truncated moment problem (TMP) on curves of the form $ y=q(x) $ y = q (x) , $ q(x)\in \mathbb R[x] $ q (x) ∈ R [ x ] , $ \deg q\geq ~3 $ deg ⁡ q ≥ 3 and $ yx^\ell =1 $ y x ℓ = 1 , $ \ell \in \mathbb N\setminus \{1\} $ ℓ ∈ N ∖ { 1 }. For even degree sequences, the solution based on the size of moment matrix extensions was first given by Fialkow [Fialkow L. Solution of the truncated moment problem with variety $ y=x^3 $ y = x 3 . Trans Amer Math Soc. 2011;363:3133–3165.] using the truncated Riesz–Haviland theorem [Curto R, Fialkow L. An analogue of the Riesz–Haviland theorem for the truncated moment problem. J Funct Anal. 2008;255:2709–2731.] and a sum-of-squares representations for polynomials, strictly positive on such curves [Fialkow L. Solution of the truncated moment problem with variety $ y=x^3 $ y = x 3 . Trans Amer Math Soc. 2011;363:3133–3165.; Stochel J. Solving the truncated moment problem solves the moment problem. Glasgow J Math. 2001;43:335–341.]. Namely, the upper bound on this size is quadratic in the degrees of the sequence and the polynomial determining a curve. We use a reduction to the univariate setting technique, introduced in [Zalar A. The truncated Hamburger moment problem with gaps in the index set. Integral Equ Oper Theory. 2021;93:36.doi: .; Zalar A. The truncated moment problem on the union of parallel lines. Linear Algebra Appl. 2022;649:186–239. .; Zalar A. The strong truncated Hamburger moment problem with and without gaps. J Math Anal Appl. 2022;516:126563. doi: .], and improve Fialkow's bound to $ \deg q-1 $ deg ⁡ q − 1 (resp. $ \ell +1 $ ℓ + 1) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1). This in turn gives analogous improvements of the degrees in the sum-of-squares representations referred to above. Moreover, we get the upper bounds on the number of atoms in the minimal representing measure, which are $ k\deg q $ kdeg ⁡ q (resp. $ k(\ell +1) $ k (ℓ + 1)) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1) for even degree sequences, while for odd ones they are $ k\deg q-\big \lceil \frac {\deg q}{2} \big \rceil $ kdeg ⁡ q − ⌈ deg ⁡ q 2 ⌉ (resp. $ k(\ell +1)-\big \lfloor \frac {\ell }{2} \big \rfloor +1 $ k (ℓ + 1) − ⌊ ℓ 2 ⌋ + 1) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1). In the even case, these are counterparts to the result by Riener and Schweighofer [Riener C, Schweighofer M. Optimization approaches to quadrature:a new characterization of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions. J Complex. 2018;45:22–54., Corollary 7.8], which gives the same bound for odd degree sequences on all plane curves. In the odd case, their bound is slightly improved on the curves we study. Further on, we give another solution to the TMP on the curves studied based on the feasibility of a linear matrix inequality, corresponding to the univariate sequence obtained, and finally we solve concretely odd degree cases to the TMP on curves $ y=x^\ell $ y = x ℓ , $ \ell =2,3 $ ℓ = 2 , 3 , and add a new solvability condition to the even degree case on the curve $ y=x^2 $ y = x 2 . [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 control method for surge instability of the compressor system. Due to the importance of the active control approach in improving the efficiency of the compressor system, a new scheme based on the model predictive control (MPC) technique has been considered to control surge which gives the benefits of control signal optimization by considering the constraints on states and input. Because of designing a novel MPC by using of linear matrix inequality scheme, the optimization problem is solved in less time and with less complexity. The proposed method is able to consider the limitation of the close coupled valve actuator and also covers the uncertainty on the model. In addition, the developed model describes the nonlinear behaviour of the compressor system and handles the effects of the pipe on surge instability. Using Lyapunov theory, the stability of the closed-loop system under the proposed robust active controller is shown. The simulation results show the high pressure and high efficiency operation of the system under study in different operating conditions. [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]

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]

In this paper, we first present multiple numerical simulations of the anti-symmetric matrix in the stability criteria for fractional order systems (FOSs). Subsequently, this paper is devoted to the study of the admissibility criteria for descriptor fractional order systems (DFOSs) whose order belongs to (0, 2). The admissibility criteria are provided for DFOSs without eigenvalues on the boundary axes. In addition, a unified admissibility criterion for DFOSs involving the minimal linear matrix inequality (LMI) variable is provided. The results of this paper are all based on LMIs. Finally, numerical examples were provided to validate the accuracy and effectiveness of the conclusions. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of integral sliding mode disturbance observer (ISDOB)-based preview repetitive control (PRC) for a class of nonlinear systems subject to external disturbances and nonlinearity. First, an ISDOB-based PRC law is presented to estimate and compensate the exogenous disturbances and nonlinearity. Next, by using a new equality constraint, a continuous-discrete two-dimensional (2D) system is established. Then, the stability of the combined controller-observer system is derived on the basis of a Lyapunov analysis, 2D system theory, and the singular-value-decomposition technique. By solving an linear matrix inequality (LMI), the gains of the controller and state observer can be obtained. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the proposed method. [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 proposes a fault tolerant control scheme for nonlinear systems in descriptor form. The approach is based on the design of an unknown input observer in order to estimate the missing state variables as well as actuator faults, such design is carried out once a proper estimation error system is obtained via a recent factorization method; then, the estimated signals are employed in the control law in order to drive the states asymptotically to the origin despite actuator faults. The designing conditions are given in terms of linear matrix inequalities. Numerical as well as physical systems are used to illustrate the advantages of the proposal. [ABSTRACT FROM AUTHOR]

This study focuses on the problem of perturbation suppression and tracking control of nonlinear fractional order systems with time‐varying delay. To simplify the control process for such systems, the Takagi–Sugeno fuzzy model is used to describe the nonlinear fractional order delayed systems. Additionally, a modified repetitive controller is applied to develop an output feedback technique for the proposed systems. To ensure system stability, the study establishes new delay‐dependent stabilization conditions using a novel Lyapunov–Krasovskii functional (LKF). These stability conditions are expressed in formation of linear matrix inequalities (LMIs) by adopting a frequency‐distributed model transformation and some slack matrices. The proposed method demonstrates that the system output can track the desired input with ignorable error, while effectively rejecting disturbances. Finally, the efficacy of the proposed method is evaluated through simulations of the modified Chua circuit and the hydraulic turbine governing system (HTGS). [ABSTRACT FROM AUTHOR]

Networked control system (NCS) is widely used in various fields, but the nonlinear of the controlled plants and the limited network bandwidth bring stability issues, which will affect the performance or even instability of the NCS. To address these aforementioned challenges, this paper proposes a novel nonlinear NCS framework, by considering network‐induced delay, adaptive event‐triggered mechanism, state quantization, control input quantization, and external disturbance based on T‐S fuzzy model. Also, based on this framework, we derive an H∞$$ {H}_{\infty } $$ stability criterion for NCS using linear matrix inequality and propose a collaborative design method for event triggers and controllers. Finally, we verify the superiority and effectiveness of the method by giving two numerical examples. [ABSTRACT FROM AUTHOR]

This paper addresses the problems of passivity and robust passivity for a class of stochastic switched inertial neural networks (SSINNs) with time‐varying parametric uncertainties. First, the original inertial neural networks can be converted into first‐order differential systems using a suitable variable transformation approach. Moreover, by using a proper Lyapunov–Krasovskii functional (LKF) theory, Jensen's inequality, and the state‐dependent switching (SDS) law approach, several adequate criteria are derived in terms of linear matrix inequalities (LMIs) to ensure passivity and robust passivity analysis of SSINNs with parametric uncertainties and time‐varying delays. It is demonstrated that the developed SDS law may guarantee the passivity requirements of the above‐considered system made up of all unstable subnetworks. Furthermore, the gains are obtained by solving a set of LMIs that can be easily verified by some standard numerical packages. Ultimately, two examples with numerical simulations are provided to demonstrate the efficacy and feasibility of the suggested method. [ABSTRACT FROM AUTHOR]

This paper designs a decentralized sliding mode preview repetitive control (SMPRC) for interconnected nonlinear systems. First, an augmented error system, which is composed of the derivative equation of the available future reference dynamics, the output of the modified repetitive controller and the tracking error dynamics, is constructed. Next, an integral switching surface is designed to verify the robust asymptotic stability of the considered system subject to nonlinearity. Then, the preview repetitive-control (PRC) law design problem is transformed into the stability problem of the augmented system considering the nominal conditions. Thereafter, a sliding mode control (SMC) law cooperates with the PRC law with the purpose to ensure the robustness of the interconnected systems in the presence of nonlinearity. Further, the required stability conditions are derived on the basis of a Lyapunov analysis, linear matrix inequalities (LMI) and the singular-value-decomposition (SVD) technique. Finally, the numerical simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper analyzes the problem of simultaneous fault detection and control of the six-rotor unmanned aerial vehicle control system, considering external disturbance, measurement disturbance, and actuator fault. The integral event trigger mechanism is introduced in the control side and sensor side of the system. Based on Lyapunov stability and H∞ control theory, the sufficient conditions to make the fault system asymptotically stable and have certain performance indexes are given by means of linear matrix inequalities; at the same time, the design criteria of event trigger parameters are also given. The linear matrix inequality is decoupled, and the calculation method of gain matrix of simultaneous fault detection and control module is given. The effectiveness of the proposed method is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

This article studies the output feedback H∞$$ H\infty $$ control problem for event‐triggered Markovian jump networked control systems with signal quantization. First, a Lyapunov–Krasovskii function is constructed, which contains time delay, upper bound of time delay and conditional transition probability information of Markovian jump systems. Second, when using the Wirtinger's inequality and the Reciprocally convex inequality to estimate the upper bound of the delay of the weak infinitesimal generator operator of the Lyapunov–Krasovskii function, the event‐triggered scheme and the signal quantization scheme are introduced. Finally, the stability criterion of the closed‐loop system of event‐triggered Markovian jump networked control systems and the design method of the output feedback controller of H∞$$ H\infty $$ disturbance attenuation level γ$$ \gamma $$ are given in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is verified by two numerical examples. [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 accuracy of curved path-tracking for headland turning of transplanters is crucial to maintaining the row spacing precision required for rice planting. To address this issue, a method based on H-infinity state feedback control is proposed. In this method, the requirement of robustness is transformed into linear matrix inequalities (LMIs) to optimize the gain coefficients of the control law. The simulation test show that this method outperforms the Linear Quadratic Regulator (LQR) when facing uncertain parameters (longitudinal speed and cornering stiffness) and path curvature disturbance. In addition, the field test results show that when the transplanter tracks a 1/4 circular arc path with a radius of 2 meters, the mean value of the absolute lateral error and the absolute heading angle error using this controller are 0.029 m and 3.69°, respectively. The maximum absolute lateral error is 0.072 m, and 64% of the absolute lateral error are less than 0.04 m, meeting practical requirements. Compared with the LQR controller with feed forward control, the mean value of the absolute lateral error is reduced by 36%. This method meets the accuracy and robustness requirements for unmanned rice transplanter turning at the headland. [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]

Summary: This paper deals with observer‐based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time‐varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full‐rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real‐time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer‐based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time‐varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed‐loop system, which optimizes the design scheme of the fault‐tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations. [ABSTRACT FROM AUTHOR]

In this paper, a fault estimation technique is proposed for discrete-time nonlinear interconnected systems with uncertain interconnections. To achieve the fault estimation, the decentralized fuzzy observer is adopted based on the Takagi–Sugeno fuzzy model. Based on the estimation error model with the subsystems of the interconnected system and its decentralized fuzzy observer, the fault estimation condition with H ∞ performance is presented. The main idea of this paper is that a novel inequality condition for H ∞ performance is used, and the sufficient condition is presented to guarantee the good fault estimation performance. Also, the decentralized fuzzy observer design condition for the fault estimation is converted into linear matrix inequality formats. Finally, a simulation example is provided, and the effectiveness of the proposed fault estimation technique is verified by comparison of the fault estimation performance. [ABSTRACT FROM AUTHOR]

This paper proposes a learning-based control approach for autonomous vehicles. An explicit Takagi–Sugeno (TS) controller is learned using input and output data from a preexisting controller, employing the Adaptive Neuro-Fuzzy Inference System (ANFIS) algorithm. At the same time, the vehicle model is identified in the TS model form for closed-loop stability assessment using Lyapunov theory and LMIs. The proposed approach is applied to learn the control law from an MPC controller, thus avoiding the use of online optimization. This reduces the computational burden of the control loop and facilitates real-time implementation. Finally, the proposed approach is assessed through simulation using a small-scale autonomous racing car. [ABSTRACT FROM AUTHOR]

A robust dynamic output feedback predictive control approach is developed for a discrete system with time-varying delays, unknown external disturbances, and unmeasurable states. First, the discrete system is transformed into an incremental state deviation model. Based on this model, a novel tracking deviation feedback model is established by extending the output tracking error. Then, a robust predictive control law, possessing more degrees of freedom, is designed. The closed-loop model is further given in conjunction with the feedback model. Second, by using the linear matrix inequality (LMI) method, relaxation technique, and variable transformation method, a less conservative stability condition is given in LMI form, which allows the controller to tolerate a greater range of time-varying delays. The gains of the control law are acquired by solving the stability condition, and the control performance can be significantly enhanced. Finally, by utilizing the TTS20 water tank as a simulation case, the viability and effectiveness of the proposed method are demonstrated. [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 investigates the positive realness of continuous fractional-order (FO) two-dimensional (2D) Roesser model with the FO ρ 1 ∈ (0 , 1 ] , ρ 2 ∈ (0 , 1 ] . A sufficient condition that ensures that the continuous FO 2D Roesser model is stable and positive real is given as linear matrix inequalities (LMIs). Then, the positive real control problem for continuous FO 2D Roesser model with state feedback and dynamic output feedback controllers is addressed. The sufficient conditions are given in LMI form, and the parameters of the controllers can be achieved from the solution of the LMIs easily. Finally, the validity of the results is checked by several examples. [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 investigates the model predictive control (MPC) for the trajectory tracking of the unmanned vehicle system with bounded disturbances and actuator saturation based on the unscented Kalman filter (UKF). In order to obtain accurate system state, the linear matrix inequality (LMI)-constrained UKF is addressed by solving the LMI optimization problem. Moreover, by expressing the saturating linear feedback law as convex hull and describing the stability of the vehicle kinematics model with bounded disturbance via the quadratic bounded theorem, a model predictive controller to achieve trajectory tracking is proposed by solving the infinite horizon optimization problem. The effectiveness of the proposed approach is verified by the co-simulation platform of Matlab/Simulink and Carsim. The results of simulations show that this approach can improve the accuracy of state estimation as well as the trajectory tracking control. [ABSTRACT FROM AUTHOR]

The paper presents a nonlinear field-oriented control technique based on the tensor product representation of the nonlinear induction machine model and the solvability of linear matrix inequalities. The nonlinear model has 32 quasi linear parameter-varying equivalent variants, and it is shown that only half of the models result in feasible controller. Two control goals are realized: torque control and speed control. The controller is a nonlinear state feedback controller completed by integral action. A new block diagram is investigated for speed control. The controller gains are designed by the solution of linear matrix inequalities to solve the Lyapunov inequality to obtain a stable and fast response and constraints on the control signal. The presented methods are verified and compared by simulations. [ABSTRACT FROM AUTHOR]

The problem of consensus control of linear discrete-time multi-agent systems (MASs) with switching topology is considered in the presence of a leader. The goal of consensus control is to bring the states of all agents to the leader state while providing stability for local agents, as well as the MAS as a whole. In contrast to the traditional approach, which uses the concept of an extended dynamic multi-agent system model and communication topology graph Laplacian, this paper proposes a decomposition approach, which provides a separate design of local controllers. The control law is chosen in the form of distributed feedback with discrete PID controllers. The problem of local controllers’ design is reduced to a set of semidefinite programming problems using the method of invariant ellipsoids. Sufficient conditions for agents’ stabilization and global consensus condition fulfillment are obtained using the linear matrix inequality technique. The availability of information about a finite set of possible configurations between agents allows us to design local controllers offline at the design stage. A numerical example demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Uncertain grid impedance is often common in power distribution networks; therefore, it is crucial to design an efficient controller in this situation. An issue that frequently occurs is the problem of unpredictable grid impedance, which can cause voltage fluctuations, power quality problems, and potential damage to equipment. This work provides a systematic control strategy to tackle these issues by supplying well-regulated power from a DC source to an AC power grid. A linear matrix inequality (LMI)- based robust optimal control is proposed in this paper to provide stability to the inverter system without offset error at the output side. The convergence time to steady state is minimized by solving the LMI problem to maximize the eigen value of the closed-loop system with the inclusion of the uncertainty of the filter parameter and grid impedance. Furthermore, the uncertainties in this study include the potential variation of values for the filters and the grid's impedance. These uncertainties occur because the grid impedance can fluctuate fast in the event of a fault or termination of a transmission line, while the filter's impedance can also be affected by changes in operating temperature. The simulation study of this proposed control includes a comparison between wide and narrow uncertainty ranges, as well as a performance comparison under uncertain parameters. Furthermore, this approach exhibits a lower power ripple in comparison to existing PI control method. [ABSTRACT FROM AUTHOR]

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua's circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm's robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security. [ABSTRACT FROM AUTHOR]

Expanding upon the well-established Takagi–Sugeno (T–S) fuzzy model, the T–S fuzzy descriptor model emerges as a robust and flexible framework. This article introduces the development of optimal and robust-optimal controllers grounded in the principles of stability control and fuzzy descriptor systems. By transforming complicated inequalities into linear matrix inequalities (LMI), we establish the essential conditions for controller construction, as delineated in theorems. To substantiate the utility of these controllers, we employ the rotary inverted pendulum as a testbed. Through diverse simulation scenarios, these controllers, rooted in fuzzy descriptor systems, demonstrate their practicality and effectiveness in ensuring the stable control of inverted pendulum systems, even in the presence of uncertainties within the model. This study highlights the adaptability and robustness of fuzzy descriptor-based controllers, paving the way for advanced control strategies in complex and uncertain environments. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of stabilization of nonlinear fractional order time-delay systems in the presence of fault. A general class of nonlinear fractional order systems is considered in which fault causes variations in the system dynamic and actuators. Besides, time-varying delay is noticed in the system equations that is of high importance in control of real-life systems. In order to facilitate the problem of controller design for such systems, a precise method for modeling complex nonlinear systems, namely, Takagi–Sugeno fuzzy model, is adopted. Regarding a Caputo derivative–based Lyapunov–Krasovskii functional, new delay-dependent stabilization conditions are established in the form of linear matrix inequalities. Eventually, two examples including a truck–trailer and Lorenz system are simulated in order to evaluate the results of this research work. [ABSTRACT FROM AUTHOR]

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the issue of Robust Fuzzy Model Predictive Control (RFMPC) of nonlinear discrete‐time systems in the presence of disturbance. To this end, Takagi‐Sugeno (T‐S) fuzzy model is adopted in order to characterize uncertain nonlinear systems and facilitate providing controller for such systems. Non‐parallel distributed compensation (non‐PDC) technique is applied to design improved RFPMC with better performance. The optimization problem of RFMPC is represented in terms of linear matrix inequalities (LMIs) so as to decrease online computational burden. Besides, feasibility and stability which are decisive factors in MPC theory are investigated for the proposed method. Ultimately, two examples including cart‐damper‐spring system are simulated to evaluate the results of this research work. [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]

To enhance the stability of the frequency at the sending terminal of the HVDC island during operation, a novel DC supplemental frequency robust controller is proposed in this paper. The proposed controller utilizes the fast controllability of a DC power supply to maintain system frequency stability. The identification of a low-order linearized model of the system can be obtained from a high-precision Prony algorithm based on the second derivative method (SDM). Subsequently, utilizing a robust design methodology based on linear matrix inequalities, an additional frequency robust controller is devised, striking a balance between optimal performance and robustness. This supplementary frequency robust controller exhibits a straightforward control structure with a modest order, making it readily implementable. Simulation experiments conducted within the PSCAD/EMTDC framework substantiate that the designed supplemental frequency robust controller significantly enhances the frequency stability of the sending terminal system. Furthermore, when compared with traditional proportional integral (PI) controllers, it demonstrates superior control efficacy and robustness against various types of faults under different operational modes. Even in interconnected operational modes, it continues to operate effectively. The research findings offer valuable insights for practical applications in islanded power systems. [ABSTRACT FROM AUTHOR]

This study aims to analyze the finite-time stability performance of both non-delayed and delayed fractional-order neural networks. Our primary aim is to investigate the finite-time stability characteristics by introducing a novel inequality designed for estimating the settling time. This fresh inequality serves as the foundation for establishing sufficient criteria, formulated as linear matrix inequalities, which guarantee the finite-time stability of both non-delayed and delayed fractional-order neural networks. Additionally, we underscore the importance of incorporating comprehensive information regarding the lower and upper bounds of the activation function, especially in the context of the proposed non-delayed model. Unlike the previous works, in this paper, the linear matrix inequality technique has been adopted towards the finite-time stability behavior of the proposed model. At last, some numerical examples are examined to validate the efficacy and conservatism of the presented approach and established theoretical results over the existing literature. [ABSTRACT FROM AUTHOR]