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This article proposes a robust cooperative distributed secondary control strategy for dc microgrids, with the main focus on reducing communication burdens. To this end, we adopt a sparsity-promoting consensus-based distributed secondary control framework for converter-interfaced dc microgrids consisting of multiple distributed generation (DG) units. The proposed control strategy relies on less (sparse) information exchange over a communication network and does not require exchanging voltage signals or their estimated values amongst neighboring DG units. Rigorous Lyapunov-based stability certificates for dc microgrids are derived. The stability conditions can be verified without the knowledge of distribution lines connecting different DG units. The effectiveness of the proposed secondary control approach is verified by experimental results and a comparative simulation case study on a multiple-DG dc microgrid. [ABSTRACT FROM AUTHOR]

The stability issue of stochastic hybrid systems against energy-constrained denial-of-service (DoS) attacks is investigated in this article. A sampled-data-based Round-Robin protocol, which sends measurement data cyclically according to the predetermined transmission sequence, is introduced to avoid communication network congestion. Additionally, a new switched time-delay stochastic closed-loop system with an unstable subsystem is established by discussing the effect of DoS attacks. Then, the stability of the closed-loop system is discussed in light of the piecewise Lyapunov–Krasovskii functional method and stochastic analysis technique. Finally, two examples are included to illustrate the correctness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates the dissipative synchronization of complex dynamical networks (CDNs) with semi-Markov switching topological structures. First, by introducing a semi-Markov process, the model we investigated is more practical and stands for an extension of the Markov jump CDNs that have been widely studied. Second, an adaptive event-triggered sampling controller is newly proposed for semi-Markov jump CDNs, unlike the periodic event-triggered control scheme, the adaptive event-triggered sampling control strategy can further reduce the controller’s update frequency by adaptively adjusting its threshold. Moreover, with the help of a novel two-sided looped-functional and some advanced inequality techniques, the conservatism of the obtained result is greatly reduced. A sufficient synchronization condition that ensures the stochastic stability of the error system is established. Finally, to show the validity and superiority of the proposed method, several examples including some comparisons and applications are given in the simulation part. [ABSTRACT FROM AUTHOR]

This article focuses on the stability analysis and control design of an interval type-2 sampled-data fuzzy-model-based output-feedback (IT2SDFMBOF) tracking control system, which is formed by the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the stable reference model, and the interval type-2 sampled-data output-feedback (IT2SDOF) fuzzy controller. The design goal is to establish a proper IT2SDOF fuzzy controller that is able to drive the states of the nonlinear plant subject to uncertainties to track those of the stable reference model, and the $H_\infty$ performance index is adopted to optimize the tracking control performance. To improve the robustness of the IT2SDOF fuzzy controller against uncertainties of the nonlinear plant, IT2 fuzzy sets are utilized. Considering that the tracking control system is sampled-data (SD) type, a two-sided looped-functional-based approach exploiting the information on the interval from time $t_k$ to $t$ and the interval from time $t$ to $t_{k+1}$ is applied to enhance the stability analysis. The imperfect premise matching (IPM) concept permits the number of rules and the premise membership functions of the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be different, which can be employed to promote the design flexibility. The tracking control system with the SD type and IPM design will cause the membership grades between the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be mismatched. In addition, the membership-function-dependent stability analysis approach that can introduce the boundary information of membership functions into the stability analysis is used to relax the stability conditions. The relaxed stability conditions subject to the $H_\infty$ performance building on the Lyapunov stability theory are developed in terms of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed IT2SDFMBOF tracking control system. [ABSTRACT FROM AUTHOR]

This article investigates the stability analysis and stabilization problems for fractional-order T–S fuzzy systems via fuzzy Lyapunov function method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions cannot be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, the sliding mode control issue is investigated for a class of discrete-time Takagi–Sugeno fuzzy networked singularly perturbed systems via an observer-based technique. Moreover, to process the measurement output and schedule the transmission sequence for relieving the communication burden, a logarithmic quantizer and a weighted try-once-discard protocol are synthesized, which can further improve the network bandwidth utilization in networked control systems. Based on the fuzzy observer states, a novel fuzzy sliding surface is established by considering the singularly perturbed parameter properly, and we endeavor to synthesize a sliding mode control law such that the reachability of the prescribed sliding surface could be guaranteed. In addition, by virtue of the convex optimization theory and Lyapunov approach, sufficient conditions are developed to guarantee the asymptotic stability of the sliding mode dynamics as well as the error system with an expected $H_{\infty }$ performance. Finally, a verification example is presented to illustrate the feasibility and effectivity of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a modified way to compute open loop control for the state transfer problem (STP) for a linear time-invariant system. Solving STP analytically is a cumbersome task. This is mainly due to tedious computations of state-transition matrix and controllability Gramian matrix. The proposed modified method enables to find control law easily and with less computations. This approach is applicable even for a third-order or higher order system with single input case analytically and without use of computer. Moreover, the proposed approach minimizes the use of calculator and thereby reduces the computational rounding-off errors. Finally, it is shown that for some special case with knowledge of mode vector, the STP can be solved very quickly without even calculating the state-transition matrix and controllability Gramian matrix. Furthermore, theoretical as well as experimental evaluation of control law is provided. Experimental results are used to validate the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates the state estimation issue of discrete-time Takagi–Sugeno fuzzy Markov jump affine systems that cover both traditional fuzzy Markov jump systems and fuzzy affine systems as two special cases. The original system is transformed into a Markov jump piecewise-affine system that varies with different operating regions. The fuzzy rules are dependent on the system mode, and accordingly, the partition of the state space is mode dependent. To analyze the stochastic stability of the estimation error system, a novel mode-dependent piecewise Lyapunov function is constructed, in which the region indices of both the plant state and the estimator state are mode dependent. Then, the existence for a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the $\mathcal {S}$ -procedure and ellipsoidal outer approximation such that the estimation error system is stochastically stable with a prescribed $\mathcal { H}_{\infty }$ performance. In the end, an illustrative example of a tunnel diode circuit is adopted to showcase the effectiveness and practicability of the developed state estimation strategy. [ABSTRACT FROM AUTHOR]

This article proposes three new methods to enlarge the feasible region for guaranteeing stability for generalized neural networks having time-varying delays based on the Lyapunov method. First, two new zero equalities in which three states are augmented are proposed and inserted into the results of the time derivative of the constructed Lyapunov–Krasovskii functionals for the first time. Second, inspired by the Wirtinger-based integral inequality, new Lyapunov–Krasovskii functionals are introduced. Finally, by utilizing the relationship among the augmented vectors and from the original equation, newly augmented zero equalities are established and Finsler’s lemma are applied. Through three numerical examples, it is verified that the proposed methods can contribute to enhance the allowable region of maximum delay bounds. [ABSTRACT FROM AUTHOR]

This article focuses on investigating the synchronization and position/force tracking performance of the multilateral teleoperation system with asymmetric time delays. First, the synchronization and tracking error signals are proposed to transform the nonlinear dynamic system into a closed-loop system governed by the Markovian jumping parameter. Because of the presence of time delays, the information regarding the system states might become unavailable. Owing to this, a feedback control based on the hidden Markov model is developed through which the information on the current state of the actual system can be accessed through a series of observations. Moreover, the forward and backward delays of the master and slave manipulators are assumed to be asymmetric and varying with time. For the stability analysis, the Lyapunov–Krasovskii technique has been adopted for which its derivatives are dealt by employing Jensens’ inequality and extended reciprocal convex matrix inequality. Finally, simulation results were provided to validate the proposed methodology guaranteeing the closed-loop system to be asymptotically stable. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of real-time reachable set (RS) control for a class of singular Markov jump (SMJ) networked cascade systems with time-delay, disturbance and non-zero initial conditions. Aiming at the shortcoming that the output of the controlled object is non-zero disturbance in single loop feedback control, an SMJ networked cascade control system model is proposed. By utilizing the Lyapunov stability theory, the linear matrix inequality technique and the free-weighting matrix method, the sufficient stability conditions and the real-time RS boundary for the closed-loop stochastic systems are obtained. Then, the gains of the cascade controller are represented by a reasonable matrix decoupling method. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

In this article, stability analysis and controller synthesis problems for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay are studied. A generalized parameter-dependent reciprocally convex inequality (GPDRCI) is presented to handle the derivative of triple integral terms, which is more general than some existing ones. By choosing suitable flexible polynomials with tunable parameters, novel flexible polynomial-based functions (FPFs) are proposed in delay-product types, which overcome the incompletely slack matrices, higher-order time delay and insufficient parameters in the existing functions. Benefitting from completely slack matrices and lower-order time delay, coupling relationship among system states and time delay is fully linked. Based on the GPDRCI and FPFs, a stability condition is derived for T–S fuzzy systems. Based on the stability criterion, considering both the time-varying delay and its bounds, a generalized memory controller is designed for T–S fuzzy systems, which covers the memoryless and traditional memory ones as its special cases. In addition, the constraints on introduced slack matrices in some existing works are avoided with the help of a matrix inequality decoupling technique. These provide extra free dimensions in the solution space. Some examples are employed to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Due to the importance of reliability and security in dc microgrids, it is essential to provide maximum resilience against cyberattacks. However, insufficient global information in the microgrid makes it difficult to accurately identify the location of these attacks. To address these issues, this article develops a novel resilient distributed control mechanism, which ensures average voltage regulation and proportional load sharing in dc microgrids under unknown cyberattacks. The proposed resilient control design does not require any information regarding the nature or location of the attacks. By virtue of a graph theoretical approach and a Lyapunov-based framework, the proposed resilient distributed control strategy is designed in a way such that the system stability is always guaranteed following a comprehensive design mechanism. Finally, the robustness of the proposed resilient distributed control approach is demonstrated via simulations and validated by experimental results. [ABSTRACT FROM AUTHOR]

In this article, the multisynchronization issue of coupled memristive neural networks (CMNNs) with unbounded time delays is investigated. To begin with, a class of generalized Gaussian-wavelet-type activation functions is adopted to extend the number of stable equilibrium states. On this basis, a distributed impulsive controller is constructed to realize the multiple synchronization of the delayed CMNNs. Under the concepts of $\mu $ -stability, Filippov solution, and differential inclusion, some sufficient conditions are derived such that the addressed system can possess $(2r + 1)^{n}\,\,\mu $ -stable synchronization manifolds. The convergence performance of solutions is determined by the time delays. As the time delays increase, the stability of synchronization manifolds will transform from exponential stability to power-stability, log-stability, or log–log-stability as special cases. Moreover, considering the modeling error and external disturbance, we further investigated the multisynchronization of delayed CMNNs with parametric uncertainties and stochastic perturbations, and some robust multisynchronization criteria are obtained. Finally, the effectiveness of the obtained results is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we study the distributed resilient cooperative control problem for directed networked Lagrangian systems under denial-of-service (DoS) attacks. The DoS attacks will block the communication channels between the agents. Compared with the existing methods for the linear networked systems, the considered nonlinear networked Lagrangian systems with asymmetric channels under DoS attacks are more challenging and still not well explored. In order to solve this problem, a novel resilient cooperative control scheme is proposed by using the sampling control approach. Sufficient conditions are first derived in the absence of DoS attacks according to a multidimensional small-gain scheme. Then, in the presence of DoS attacks, the proposed resilient scheme works in a switching manner. Inspired by multidimensional small-gain techniques, the Lyapunov approach is used to analyze the closed-loop system, which enables us to establish sufficient stability conditions for the control gains in terms of the duration and frequency of the DoS attacks. [ABSTRACT FROM AUTHOR]

We present a formation control algorithm for double-integrator agents, where the formation is time-varying and the agents’ controls satisfy a priori bounds (e.g., the controls can accommodate actuator saturation). We assume that each agent has relative-position-and-velocity feedback of its neighbor agents, where the communication structure is a quasi-strongly connected graph, and at least one agent has a measurement of its position and velocity relative to the leader (if applicable). The main analytic results provide sufficient conditions such that all agents converge to the desired time-varying relative positions with one another and the leader and have a priori bounded controls (if applicable). Next, we extend the formation control algorithm to include collision-avoidance terms that, for a set of initial conditions, prevent each agent from colliding with the agents in its neighbor set or colliding with the leader (if applicable). Finally, we present results from rotorcraft experiments that demonstrate the algorithm with time-varying formations and bounded controls. These experimental results include indoor experiments using a motion-capture system and outdoor experiments demonstrating the algorithm in a real-world environment with disturbances (e.g., wind) and only onboard feedback. [ABSTRACT FROM AUTHOR]

This article addresses the investigation of sliding-mode control (SMC) for slow-sampling singularly perturbed systems (SPSs) with Markov jump parameters. As a new attempt, the SMC strategy is considered in the study of discrete-time Markov jump SPSs. Subsequently, in order to design a sliding-mode controller to ensure the stability of the proposed system, a novel integral sliding surface is constructed, and an SMC law is synthesized to ensure the reachability of the sliding surface. Through the utilization of Lyapunov stability and SMC theory, sufficient conditions are derived to ensure the state trajectories of the system are driven to a predefined sliding surface and the closed-loop sliding mode dynamics are stochastically stable. Finally, the applicability of the proposed SMC strategy is verified by a numerical example and a practical electric circuit model. [ABSTRACT FROM AUTHOR]

This brief investigates the tracking control problem of the quadrotor unmanned aerial vehicle considering the disturbance and input saturation. According to the hierarchical control principle, the quadrotor dynamics is decomposed into position and attitude loops to accommodate the controller design. To overcome the disturbance, two disturbance observer-based state estimators are designed in two loops, respectively. By integrating the filtering-error compensation mechanism and auxiliary control system into the dynamic surface control, the input saturation and filtering errors can be solved. In addition, the tracking errors of the closed-loop system can converge to the origin. Finally, simulation results show the validity of the proposed control formulation. [ABSTRACT FROM AUTHOR]

Rectified linear unit (ReLU) networks have become widely used in machine learning and automated inference using neural networks. Various forms of hardware accelerators based on ReLU networks have also been under development. In this brief, the stability problem in analog ReLU networks is addressed. Using the Lyapunov stability theory, it is shown that the origin of an unforced, analog ReLU dynamical system is globally asymptotically stable if the induced Euclidean norm of its connectivity matrix is less than one. An example is given to demonstrate that this upper bound is the best that can be achieved. In particular, the stability result holds for the case of a nonsymmetric connectivity matrix as may occur in some mathematical models of neurobiology. [ABSTRACT FROM AUTHOR]

In this article, the $H_{\infty }$ control problem is investigated for a class of discrete-time singularly perturbed systems (DTSPSs) with time-delays and sensor saturations. In order to save the network bandwidth with satisfactory communication reliability during the signal transmissions, a dynamic event-triggered mechanism (DETM) is put forward to regulate the data-packet transmissions from the saturated sensors to the proposed controller. By constructing a novel Lyapunov–Krasovskii functional dependent on the singular perturbation parameter (SPP), the dynamics of the DTSPSs under the DETM are rigorously analyzed, and an output-feedback controller design scheme is then developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed $H_{\infty }$ performance index. By resorting to the convex programming techniques, the desired controller gain is parameterized in light of the feasible solutions to a set of matrix inequalities. Finally, the effectiveness and merits of the proposed algorithm are demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

An observer-based dissipativity control for Takagi–Sugeno (T–S) fuzzy neural networks with distributed time-varying delays is studied in this article. First, the network channel delays are modeled as a distributed delay with its kernel. To make full use of kernels of the distributed delay, a Lyapunov–Krasovskii functional (LKF) is established with the kernel of the distributed delay. It is noted that the novel LKF and delay-dependent reciprocally convex inequality plays an important role in dealing with global asymptotical stability and strict $(\mathcal{Q}, \mathcal{S},\mathcal{R})$ - $\alpha $ -dissipativity of the T–S fuzzy delayed model. Through the constructed LKF, a new set of less conservative linear matrix inequality (LMI) conditions is presented to obtain an observer-based controller for the T–S fuzzy delayed model. This proposed observer-based controller ensures that the state of the closed-loop system is globally asymptotically stable and strictly $(\mathcal{Q}, \mathcal{S},\mathcal{R})$ - $\alpha $ -dissipative. Finally, the effectiveness of the proposed results is shown in numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T–S fuzzy model. First, in order to reduce the frequency of state transmission for alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we show that a fuzzy system of relative degree two can be stabilized by proportion-integration-differentiation (PID) sliding mode control depending on the outputs and their derivatives. The main focus of this article is to formulate a novel event-based fuzzy PID sliding surface under the imperfect premise matching. First, the measured output is adequately sampled for frequently checking a delay-dependent event-triggered condition, which reduces the number of data transmissions and controller updates. Then, an artificial time-delay estimator is used to approximate the output derivative. Based on linear matrix inequalities, a heuristic algorithm is investigated to design an event-triggered sliding mode controller, which reveals how to choose the maximum sampling interval that maintains the estimation accuracy and preserves the stability under fast event triggering. In simulation, the effectiveness of the proposed design method is verified in a cart and pendulum system subject to system uncertainties. [ABSTRACT FROM AUTHOR]

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi–Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of observer-based dynamic event-triggered control for a networked control system (NCS) under a class of power-constrained denial-of-service (DoS) attacks that aim at impeding the network communication from time to time. First, by carefully modeling such DoS attacks as aperiodic pulse-width-modulated (PWM) jamming signals, a switching observer, adapting to the DoS attacks, is delicately constructed to deal with the unavailability of full-state information. Second, to economize the limited bandwidth resources, a dynamic event-triggered communication scheme is designed under the aperiodic DoS jamming attacks, whose duration and frequency are assumed to be restricted. Third, a switching system model with artificial state delay is formulated, which characterizes the effects of the aperiodic DoS attacks and event-triggered communication scheme in a unified framework. Then, the asymptotic stability analysis and controller/observer synthesis conditions of the resulting switching system are obtained by using a piecewise Lyapunov–Krasovskii functional approach. Furthermore, a co-design method of the dynamic triggering parameters, controller, and observer gains is presented. Finally, an example is employed to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The co-design problem of 2-D event generators and sliding mode controller (SMC) is studied in this article for the discrete-time 2-D Roesser model to reduce the communication usage between the plant and the controller. First, by resorting to the 2-D reaching law conditions, the event-based 2-D SMC schemes are proposed and a kind of horizonal/vertical independent event generator is designed. Then, the stability of the sliding-mode dynamics is analyzed and a nonlinear matrix inequality condition associated with the horizontal/vertical sliding matrices is obtained. In order to solve the derived nonlinear matrix inequality condition without introducing conservatism, a binary genetic algorithm (GA) is applied by considering a multiobjective optimization problem, which reflects the tradeoff between the convergence of the sliding-mode dynamics and the scheduling performance of the designed horizontal/vertical event generators. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed co-design approach with GA. [ABSTRACT FROM AUTHOR]

This article studies the nonfragile sampled-data filtering problems for Takagi–Sugeno fuzzy systems with uncertainties and delays. By introducing two delay-product-type terms and other augmented terms, a novel Lyapunov–Krasovskii functional containing more detailed information of time delays is constructed. With the help of some new bounding inequalities, improved stability results for the addressed systems are established. Besides, a resilient sampled-data controller is devised with less cost. Furthermore, the efficiency of the obtained criteria is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this brief, the prescribed finite-time $H_{\infty }$ problems of nonlinear descriptor systems (NDSs) with and without actuator saturation are respectively investigated. When addressing this problem of NDSs subject to actuator saturation, it is pointed out that the existing treatments for the saturation nonlinearities are not so effective. The reason is that some of them cannot ensure that the resulting closed-loop systems are impulse controllable, and others cannot make sure that the closed-loop system can achieve prescribed finite-time stable. To overcome this issue, an available and interesting treatment is proposed. The main characteristic of this treatment is that the saturation nonlinearity is decomposed into a linear form consisting of the control signal and its constant constraints. Based on this treatment, the state feedback scheme is adopted for the considered problem, and some sufficient conditions are obtained. To illustrate the efficiency of the proposed results, an example about circuit systems is provided. [ABSTRACT FROM AUTHOR]

Due to the complicated model characteristics, only a few results focusing on stability analysis have appeared on singularly perturbed descriptor systems (SPDSs). This article instead proposes an integral sliding-mode control strategy for a kind of Takagi–Sugeno fuzzy approximation-based nonlinear SPDSs under time-varying nonlinear perturbation. An appropriate fuzzy integral switching manifold that fully accommodates the system features is designed to completely reject the matched perturbation without amplifying the unmatched one. To facilitate the synthesis of the high-level controller (HLC), the sliding-mode dynamics (SMD) is transformed into an augmented form. Thanks to the adoptions of a novel singular perturbation Lyapunov function, Finsler's lemma, as well as the fixed-point principle, the existence and uniqueness of the solution and the exponential admissibility for the augmented SMD are analyzed. A solution for the designed HLC is further provided. To guarantee the sliding motion, a fuzzy integral sliding-mode controller (FISMC) is synthesized by analyzing the sliding motion reachability. An adaptive FISMC is also given to deal with the unknown upper bounds of the matched perturbation. Finally, the applicability of the developed FISMC strategy is testified by a practical example. [ABSTRACT FROM AUTHOR]

This article focuses on the design of a fuzzy adaptive event-triggered sampled-data control (AETSDC) scheme for stabilization of Takagi–Sugeno (T–S) fuzzy memristive neural networks (MNNs) with reaction–diffusion terms (RDTs). Different from the existing T–S fuzzy MNNs, the reaction and diffusion phenomena are considered, which make the presented model more applicable. A fuzzy AETSDC scheme is proposed for the first time, in which different AETSDC mechanisms will be applied for different fuzzy rules. For each fuzzy rule, the corresponding AETSDC mechanism can be promptly adaptively adjusted based on the current and last sampled signals. So the fuzzy AETSDC scheme can effectively save the limited communication resources for the considered system. By introducing a suitable Lyapunov– Krasovskii functional, new stability and stabilization criteria are established for T–S fuzzy MNNs with RDTs. Meanwhile, the desired fuzzy AETSDC gains are obtained. Finally, simulation results are given to verify the superiority of the fuzzy AETSDC scheme and the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The extended strictly positive realness of singular fractional-order systems with the fractional-order α ∈ (1,2) is investigated in this brief. Firstly, a novel sufficient and necessary condition for the extended strictly positive realness of fractional-order systems is derived in terms of linear matrix inequalities. Secondly, a novel sufficient and necessary condition for the admissibility and extended strictly positive realness of singular fractional-order systems is obtained in terms of linear matrix inequalities with equality constraints. Finally, two examples are presented to show the effectiveness of the obtained methods. [ABSTRACT FROM AUTHOR]

The synchronization of a class variable-coefficient complex networks with reaction-diffusion terms is investigated. The objective of this article is to synthesize a state-feedback controller, which is designed based on a Takagi–Sugeno (T–S) fuzzy model of the variable-coefficient complex network with reaction-diffusion terms such that the closed-loop system is synchronized. With the support of Green formula and some matrix inequality techniques, and utilizing the upper and lower bounds of the membership functions, membership-function-dependent (MFD) synchronization conditions guaranteeing the system's synchronization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is presented to verify the analysis results and illustrate the effectiveness of the proposed synchronization conditions. [ABSTRACT FROM AUTHOR]

This paper deals with the dissipative control and filtering problems for the discrete-time two-dimensional (2-D) switched Fornasini–Marchesini (FM) systems. First, the definition of 2-D TSR-θ-dissipativity for the FM systems is introduced. By employing the switched quadratic Lyapunov function technique and establishing multiple recursive formulas, sufficient conditions are developed to guarantee that the considered system is asymptotically stable under the arbitrary switching signal (ASS) case and exponentially stable under the restricted switching signal (RSS) case with the 2-D TSR-θ-dissipativity, respectively. The special cases, such as the 2-D passivity performance and the 2-D H∞ performance, are also discussed. Based on the obtained dissipative stability conditions, the 2-D TSR- θ-dissipative state feedback controller and filter design problems are further studied for the addressed system. Particularly, the extended average dwell time (define this later on in text) technique is utilized for the system under the RSS case. Finally, the effectiveness of the proposed design method is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of sliding mode controller design for a class of T–S fuzzy singular systems (TSFSSs) with partly immeasurable premise variables. By analyzing the different cases of immeasurable premise variables, novel state-feedback, and static output-feedback-based sliding mode controllers design methods are first developed. The information of measurable premise variables in TSFSS is utilized to design the controllers. Attention is focused on solving the problem of sliding mode controllers design for TSFSS with immeasurable premise variables related to time and system states. Further, based on the new sliding mode control (SMC) methods, some new convex conditions for designing sliding mode controllers are proposed. It is shown that the proposed sliding mode controllers design approaches have the advantage over existing SMC methods to stabilize the TSFSS with immeasurable premise variables. Finally, two simulation results are given to verify the feasibility and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article investigates the observer-based finite-time H∞ control problem for interconnected fuzzy systems with quantization and random network attacks, where two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered. In order to achieve the occupancy reduction of network resources, the measured outputs of interconnected systems are quantized through a logarithmic quantizer before being transmitted by the communication channel. Combining the effects of quantization and random network attacks, an observer-based control model is first constructed. Then, based on Lyapunov functional approach and stochastic analysis technique, some sufficient conditions are presented such that the considered closed-loop interconnected system is stochastically finite-time bounded with a prescribed disturbance attenuation level, and the gain matrices of fuzzy observer and fuzzy controller can be found by solving an optimization algorithm with linear matrix inequalities constraints. Finally, two simulation examples are given to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of fault detection filtering design for discrete-time interval type-2 Takagi–Sugeno (T–S) fuzzy systems in finite frequency domain. Considering the fact that external disturbances and faults are usually reside in finite frequency ranges, the finite frequency $\mathscr H_{\infty }$ and $\mathscr H_{-}$ performances are introduced to reflect the disturbance robustness and fault sensitiveness in finite frequency domain, respectively. Based on discrete-time Fourier transform and its properties, finite frequency performance analysis results are first obtained. Then, by exploiting the information on upper and lower membership functions, the membership-function-dependent filtering design conditions in the form of linear matrix inequalities are established for discrete-time interval type-2 T–S fuzzy systems in finite frequency domain. With the obtained filter, a fault detection scheme is then proposed and it is shown that the resulting fault detection system is asymptotically stable with prescribed finite frequency $\mathscr H_{\infty }$ and $\mathscr H_{-}$ performances. Finally, the effectiveness of the proposed method is validated by simulation studies. [ABSTRACT FROM AUTHOR]

This paper studies the stability analysis of the input saturated discrete-time switched systems with average dwell-time based on the parametric discrete-time Riccati equation. The state feedback controller and the observer-based output feedback controller are designed to guarantee the exponential stability of the closed-loop system. The proposed method is simple and easy to operate in practice. The designed controllers can be computed easily by solving the parametric discrete-time Lyapunov equation. The main advantages of this paper are that the stability analysis is based on the properties of the saturation function and limited structure information of the actuator saturation and that the designed controllers have good robustness to the structure uncertainty of the input saturation. The simulation results illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article investigates the sliding-mode control (SMC) problem for a class of T–S fuzzy systems with communication constraints. The weighted try-once-discard (WTOD) protocol is utilized to arrange the transmission order of actuator nodes, under which only one node is permitted to obtain access to the communication network at any time. A key issue is how to integrate the WTOD protocol into the design of the SMC system. To this end, an update rule is proposed for the actuators to obtain the actual actuator signals. And then, a membership-function-dependent (MFD) sliding surface and a token-dependent sliding-mode controller are designed. By taking the information of membership functions into stability and reachability analysis, MFD sufficient conditions are derived such that both the asymptotic stability of the closed-loop fuzzy systems and the reachability of the specified sliding surface can be guaranteed. Moreover, the cone complementary linearization (CCL) algorithm is employed to convert nonlinear inequalities into a minimization problem with linear constraints. Finally, a numerical example is utilized to illustrate the proposed SMC design approach. [ABSTRACT FROM AUTHOR]

In this article, penalty factor threshold and time step bound in discontinuous Galerkin time method based on vector wave equation (DGTD-WE) method are well estimated. Based on the semidiscrete form of the DGTD-WE method, properties of the system matrices are studied and the stability condition related to the penalty factor is derived. By decomposing the global system matrices of the DGTD-WE method into the local ones and developing an efficient iteration procedure, the lower bound threshold of the penalty factor is well estimated to guarantee the positive semidefinite property of the global system matrices. With the calculated penalty factor, the maximum time step is analytically determined by approximating spectral radius of the local system matrix. Both the penalty factor bound and the maximal time step are computed element-wise instead of a global system matrix operation, and thus, the proposed method can be efficiently applied into the large-scale meshes with different types of the basis functions and boundary conditions. Numerical examples are presented to demonstrate the validity and good performance of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the ${N}$ -step model predictive control (MPC) problem for a class of constrained systems with persistent bounded disturbances under the stochastic communication protocol (SCP). The control signals are transmitted to the plant via a shared network subject to a prescribed SCP for the purpose of avoiding data collisions. The SCP scheduling, which is governed by a Markov chain, is applied to orchestrate the transmission order of the controller nodes. Under the SCP, only one control node is allowed to update the control signal sent to the plant at each communication instant. Our aim is to design a set of desired controllers in the framework of ${N}$ -step MPC such that the mean-square input-to-state stability of the closed-loop system is guaranteed. An optimization algorithm consisting of both off-line and online parts is developed to cope with the design problem of the ${N}$ -step controller. Finally, a numerical example is utilized to illustrate the validity of the proposed ${N}$ -step MPC strategy. [ABSTRACT FROM AUTHOR]

Finite-time stability (FTS) analysis and control problems are investigated in this paper for continuous-time networked dynamical systems constituted by many subsystems. Interactions among these subsystems are arbitrary and time-varying, and every subsystem has different and time-varying dynamics. Several differential linear matrix inequality (LMI) formed methods are presented for the FTS analysis and control, which avoid the inverse computation of matrices with large dimensions and efficiently utilize the block diagonal characteristic of system parameters and the sparseness of the subsystem connection matrix. Sufficient conditions only depending on the parameters of each individual subsystem are then derived. Furthermore, LMI-based conditions are also provided for the FTS analysis and control of linear time-invariant networked systems. Numerical simulations show that they are computationally effective to analyze and synthesize a large-scale networked dynamical systems. [ABSTRACT FROM AUTHOR]

This paper addresses the control problem of the switched system with bounded actuators and average dwell-time. We present the switching rules for the designed controllers based on two kinds of parametric algebraic Riccati equation. The exponential stability of the switched system under the average-dwell time is ensured by the designed controllers and the switching rules. The dynamic performance of the control system is enhanced greatly by the proposed method. The simulation results illustrate the effectiveness and the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]