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Summary: This study investigates the ℋ∞$$ {\mathscr{H}}_{\infty } $$ secure consensus issue for Markov jump multi‐agent systems with denial‐of‐service attacks and disturbance. Considering that the mode of the system cannot be directly obtained in the actual situation, a detector is constructed to obtain the mode of the system indirectly with the help of the hidden Markov model. The network communications between agents are undirected, and denial‐of‐service attacks are encountered randomly and represented by a random variate obeying Bernoulli distribution. The reduced‐order decomposed system is obtained by the method of model reduction. On this basis, the Lyapunov stability theory is applied to derive some sufficient conditions to guarantee that the system achieves consensus with a stipulated ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance index. Finally, a numerical example is employed to verify the validity of the proposed protocol. [ABSTRACT FROM AUTHOR]

This work investigates the ℋ∞$$ {\mathscr{H}}_{\infty } $$ control problem of discrete‐time singular Markov jump systems against denial of service attacks, in which the Markov state information is seen as restricted access. To solve this situation, a hidden Markov model is introduced. The main objective is to construct a controller with the help of hidden Markov model such that the stochastically admissible of the closed‐loop singular Markov jump systems with limited access mode information can be guaranteed under denial of service attacks. To produce the needed hidden Markov model‐based controller, a matrix contract transformation approach is developed. At the end, a numerical example and a tunnel diode circuit are presented to demonstrate the effectiveness and benefit of the design technique described in this research. [ABSTRACT FROM AUTHOR]

This paper investigates the $ \mathcal {H_{\infty }} $ H ∞ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet $ \mathcal {H_{\infty }} $ H ∞ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided. [ABSTRACT FROM AUTHOR]

This article concentrates on the non‐zero‐sum games problem of discrete‐time Markov jump systems without requiring the system dynamics information. First, the multiplayer non‐zero‐sum games problem can be converted to solve a set of coupled game algebraic Riccati equations, which is difficult to be solved directly. Then, to obtain the optimal control policies, a model‐based algorithm adapting the policy iteration approach is proposed. However, the model‐based algorithm relies on system dynamics information, which has the limitations in practice. Subsequently, an off‐policy reinforcement learning algorithm is given to get rid of the dependence on system dynamics information, which only uses the information of system states and inputs. Moreover, the proof of convergence and Nash equilibrium are also given. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: The article mainly studies the fault‐tolerant control of complex networks with semi‐Markov jump topology under hybrid attacks. First, the semi‐Markov process is imported to the topology change of sampled‐data complex networks. Second, by designing a strategy to resist mixed attacks, the system can remain stable even under mixed attacks. Then, some sufficient conditions have been established to guarantee H∞$$ {H}_{\infty } $$ performance through fault‐tolerant control mechanism even if it suffers from actuator failure. Finally, a numerical example and a practical example are used to prove the feasibility of the theory. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the problem of non‐fragile H∞$$ {H}_{\infty } $$ state estimation for Markov jump complex networks with two‐time‐scale characteristics in discrete time, in which the transition probabilities information is partially known. A singular perturbation parameter reflects the two‐time‐scale property of Markov jump complex networks. The goal is to design a mode‐dependent state estimator to ensure that the estimation error system is stochastically stable and satisfies the H∞$$ {H}_{\infty } $$ performance index. By constructing a mode‐dependent Lyapunov function with the singular perturbation parameter, a sufficient condition based on the linear matrix inequality is obtained. By introducing an optimized relaxation matrix, a novel decoupling method is proposed for complex networks with two‐time‐scale characteristics to reduce the conservatism of the obtained state estimator. The usefulness of the intended state observer and the superiority of the unique decoupling approach provided are demonstrated numerically. [ABSTRACT FROM AUTHOR]

This paper investigates the control issue for interval type-2 (IT2) fuzzy singularly perturbed systems with Markov jumping parameters. In order to get closer to the practical physical systems, it is feasible to embed IT2 fuzzy logic sets in the singularly perturbed systems. The stochastic parameters and the transition probabilities contained in the systems are generated from the Markov process. Then, the IT2 fuzzy singularly perturbed systems are guaranteed to achieve the stochastic stability with an H ∞ performance by the designed controller. Afterward, some conditions are established to guarantee the stochastic mean-square stable of the system. Finally, the availability of the proposed fuzzy control scheme is verified by a numerical example. [ABSTRACT FROM AUTHOR]

This paper addresses the secure consensus control problem for a class of continuous-time two-time-scale Markov jump multi-agent systems under hybrid cyber-attacks, which suffers from both the denial-of-service attacks and deception attacks. Firstly, to make the constructed model fit the practice better, the dynamic of each agent is represented by a two-time-scale system and the transition rate matrix of the Markov chain is assumed to be partially unknown. Then, a secure consensus protocol is designed to deal with the hybrid cyber-attacks and guarantee the average consensus can be achieved with a prescribed H ∞ performance. Based on the stochastic analysis approach and Lyapunov stability method, some sufficient conditions are given in the form of linear matrix inequalities. Furthermore, the desired secure consensus protocol gains can be obtained by solving a convex optimization problem. Finally, an illustrative example is utilized to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the static output feedback secure control problem for discrete-time hidden Markov jump systems against replay attacks. The main purpose is to realise that closed-loop systems are stochastically stable with or without replay attacks. Firstly, the tampered sensors under replay attacks can be identified via the proposed detection method. Then, an asynchronous static output feedback controller is designed, which can eliminate the negative impact caused by replay attacks in view of the detection results. Based on the linear matrix inequality technique, some sufficient conditions which ensure the closed-loop systems are stochastically stable and meet a given H ∞ performance are established. Finally, a numerical example and a practical example are given to verify the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper concentrates on the problem of asynchronous ℋ∞$$ {\mathscr{H}}_{\infty } $$ filtering for singular Markov jump systems under DoS attacks, in which the unknown probability information cases are considered. To better describe cyber security problem, DoS attacks are considered as encountered randomly and modeled by a set of stochastic variables obeying Bernoulli distribution. Besides, hidden Markov model with partially known probability information is proposed to handle the cases that the Markov state information of the system is restrictedly accessed, and the transition probability information and observation probability information can not be directly obtained. A set of criteria are derived to analyze the regularity, causality, and stochastic stability for the filtering error system with an ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance index. Furthermore, an asynchronous filter design method is proposed to against DoS attacks. Finally, a numerical example and a practical example modeled by a DC motor are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This aricle investigates the passivity‐based control problem for Markovian jump singular systems with aperiodic sampling and actuator failures. Firstly, in order to fully consider the system information, two novel mode‐dependent Lyapunov–Krasovskii functions (LKFs) are constructed, which are composed of one‐sided and two‐sided looped‐functionals respectively. Based on these two LKFs and an improved integral inequality, two stochastic admissibility and robust passivity criteria with lesser conservatism are given by using linear matrix inequalities (LMIs). Moreover, through these theorems, it is proved that the positive constraint of LKFs can be relaxed from all times to sampling times for Markovian jump singular systems with aperiodic sampling and actuator failures. Then, two aperiodic sampled‐data controller algorithms are proposed by LMIs to ensure the stability of the systems. Finally, A numerical example and a model of DC motor driving an inverted pendulum are provided to demonstrate the validity of the main results. [ABSTRACT FROM AUTHOR]

This article investigates the problem of designing $\mathcal {H}_{\infty }$ dynamic output feedback reliable controller for discrete-time Markov jump nonlinear systems with persistent dwell-time switched transition probabilities based on the Tagaki–Sugeno fuzzy model. The uncertainty of measurement output, which is assumed to occur randomly, and mode-dependent actuator faults are considered simultaneously. Moreover, the jumping property presented by system modes is described by the Markov chain of which transition probabilities are considered to be piecewise time-varying, and is described by adopting the more flexible persistent dwell-time switching rule. Based on the stochastic analysis approach and Lyapunov stability theory, some sufficient conditions are established to ensure the resulting closed-loop system being mean-square exponentially stable with the prescribed $\mathcal {H}_{\infty }$ performance. Furthermore, the desired controller gains can be obtained through solving a convex optimization problem. Finally, the practicability and availability of the proposed control method are illustrated by a numerical example and a modified tunnel diode circuit model. [ABSTRACT FROM AUTHOR]

This article concentrates on the model-based fuzzy $l_{2}-l_{\infty }$ filtering problem of a discrete-time semi-Markov jump nonlinear system. The random jumps in the studied system are governed by the discrete-time semi-Markov process. Therefore, the storage characteristics of the transition probability between systems are fully considered. To analyze the $\sigma$ -mean-square stability of the filtering error system, a mode-dependent filter, which is based on the discrete-time fuzzy semi-Markov jump model, is constructed to estimate the state of the system. Thereafter, based on the Lyapunov stability theory and the discrete-time semi-Markov kernel concept, a set of sufficient criteria to ensure the $\sigma$ -mean-square stability and $l_{2}-l_{\infty }$ performance are derived. In addition, by using the Takagi–Sugeno fuzzy model, the nonlinear problem is effectively solved. Two illustrative examples, including a numerical example and a tunnel diode circuit example, are demonstrated to reveal the practicability of the developed filtering strategy. [ABSTRACT FROM AUTHOR]

This paper aims to address the fault-tolerant control problem for a class of discrete-time Takagi–Sugeno fuzzy Markov jump systems, where Markov process is introduced to represent the structural changes in system parameters. And a group of Bernoulli distributed white variables are introduced to characterize the random gain variations. Also, according to Lyapunov stability theory, a set of sufficient conditions which can achieve the mean square stochastic stability with an extended dissipative performance index of the closed-loop systems are established. In the end, the effectiveness of the method proposed in this paper is illustrated by analyzing a numerical example. [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]

In this article, the problem of reachable set estimation (RSE) and aperiodic sampled‐data controller design are considered for Markovian jump systems (MJSs) with unit‐energy bounded disturbance and unit‐peak bounded disturbance inputs. First, by constructing mode‐dependent loop‐based Lyapunov functional, the linear matrix inequalities method is used to derive sufficient conditions for all states of MJSs under zero initial conditions to be bounded by ellipsoids. Second, RSE is considered in the process of designing the aperiodic sampled‐data controller. The objective is that the resulting ellipsoid comprises the reachable set of the closed‐loop system. Finally, the effectiveness of these methods is illustrated by the actual aircraft model and simulation results in this article. Furthermore, compared with other articles through numerical comparison, the method provided in this article can obtain less conservative results. [ABSTRACT FROM AUTHOR]

This article study the asynchronous control problem for a class of discrete-time Markovian jumping Lur’e systems (MJLSs) over the finite-time interval. The partial accessibility of system modes with respect to the designed controller is described by a hidden Markov model (HMM). The asynchronous control law consists of two parts, i.e., the states and the nonlinearities involved in the dynamics of the controlled system. By selecting the appropriate Lyapunov functional and applying the modified sector condition, the finite-time stabilization conditions under the control constraints are derived. Finally, the effectiveness of the designed method is verified by an illustrative simulation. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile $\mathcal {H}_{\infty }$ synchronization issue for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markov jump systems. With regard to the T–S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed $\mathcal {H}_{\infty }$ performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of fuzzy-model-based fault-tolerant control for nonlinear semi-Markov jump systems in the discrete-time context. The discrete-time semi-Markov process is employed to describe the mode jumping among several subsystems in the investigated systems. Moreover, the nonlinear characteristics are effectively tackled through utilizing the Takagi–Sugeno fuzzy model. Unlike some previous results, the information of the semi-Markov kernel (SMK) in this article is assumed to be partially available, which conforms better with the practical scenarios. Besides, considering the case that actuators may encounter some unexpected failures during system operation, the fault-tolerant mechanism is introduced in the process of controller design to enhance the fault tolerance of the studied systems. By means of SMK approach and Lyapunov stability theory, some elapsed-time-dependent criteria for guaranteeing the mean-square stability of the closed-loop system are established. According to these criteria, the design methodology of the reliable fuzzy state feedback controller is developed. Eventually, in order to verify the practicability and rationality of the developed control scheme, a single-link robot arm model is presented. [ABSTRACT FROM AUTHOR]

In this article, passivity‐based sampled‐data control for Markovian jump systems (MJSs) with stochastic sampling is conducted by virtue of the looped‐functional approach. First, based on the input delay approach, the MJS under stochastic sampled‐data control is modeled as a time‐varying continuous‐time system with a random variable. Second, a time‐dependent looped‐functional is developed, which only requires its positive definiteness at the sampling instants and takes full use of the state information. Moreover, a free‐matrix‐based integral inequality is used to derive some less conservative passivity conditions expressed in terms of linear matrix inequality (LMIs). Meanwhile, a design algorithm for the mode‐dependent stochastic sampled‐data controller is provided. A numerical example is given to demonstrate the validity and superiority of the proposed analysis method. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile extended dissipative control problem for a class of nonlinear fast sampling singularly perturbed systems subject to Markov jumping parameters. Thereinto, the Tagaki–Sugeno fuzzy model is utilized to describe the nonlinear part, and the nonfragile control strategy is employed to handle the gain variations in a controller. Furthermore, we aim to design a fuzzy nonfragile controller, which can ensure that the systems under consideration are stochastically stable as well as extended dissipative. To this end, through constructing a mode-dependent Lyapunov function and applying the convex optimization theory, some sufficient conditions that are independent of the singular perturbation parameter $\epsilon$ are derived. Besides, a set of controller gains is also obtained by solving the aforesaid conditions. Based on the effectiveness of the controller, the technique to obtain the upper bound of the singular perturbation parameter is developed, and an improved system performance related to such an upper bound is achieved. Finally, through a numerical example and an inverted pendulum model example, the superiority and the practicability of this article are verified. [ABSTRACT FROM AUTHOR]

We investigate the problem of ℋ∞ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule, as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously. Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an ℋ∞ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the nonfragile ${\mathcal {H}_{\infty }}$ control problem for discrete-time fast sampling Markovian jump singularly perturbed nonlinear systems described by the Takagi-Sugeno fuzzy model. By utilizing singular perturbation theory, a singular perturbation parameter (SPP) independent, i.e., ${\epsilon }$ -independent, condition is derived to make sure the underlying closed-loop system’s stability and a mixed $ {\mathcal {H}_{\infty }}$ and passive performance ${\gamma }$ , simultaneously. The ill-conditioned case caused by SPP could be eliminated on the basis of such a condition. With the aid of the stochastic analysis approach, the desired controller gains can be obtained, where the nonfragile property is fully considered to improve the tolerance of controller. Furthermore, a technique is developed to estimate the upper bound of SPP $\boldsymbol {\epsilon }$ in this paper by employing a useful inequality. The availability and practicability of the proposed design method are finally explained via a practical example of a tunnel diode circuit with a modified model and a numerical example. [ABSTRACT FROM AUTHOR]

Based on the Lyapunov stability theory, this paper mainly investigates the H∞ synchronization problem for semi-Markovian jump neural networks (semi-MJNNs) with randomly occurring time-varying delays (TVDs). The continuous-time semi-MJNNs, where the transition rates are dependent on sojourn time, are introduced to make the issue under our consideration more general. One of the main characteristics of our work is the handling of TVDs. In addition to using the improved Jensen inequality and the reciprocal convexity lemma to deal with the integral inequality, we also employ Schur complement and the projection lemma to achieve the decoupling between the square term of TVDs. Finally, we verify the validity and feasibility of our method by a couple of simulation examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the energy-to-peak filtering issue for a class of singular semi-Markov jump systems with unideal measurements. Some network-induced phenomena, such as sensor nonlinearity and packet dropouts caused by the unideal measurements are considered. The occurrence of sensor nonlinearity is described in a random way and obeyed a Bernoulli distribution. In the framework of the Lyapunov–Krasovskii stability theory, some sufficient conditions are given to ensure that the considered error system is stochastically mean-square stable and guarantees an energy-to-peak (or called L 2 − L ∞ ) performance level. On the basis of these conditions, an available design method to the desired filter is proposed drawing support from an improved matrix decoupling approach. For showing the effectiveness and superiority of the proposed method, we finally provide two illustrated examples. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the reliable mixed H ∞ /passive control for Takagi–Sugeno (T–S) fuzzy delayed systems based on a semi-Markov jump model (SMJM) approach. The focus is to design a fuzzy fault-tolerant controller such that the resulting closed-loop system is stochastically stable with a prescribed mixed H ∞ /passive performance level even if the actuator failures appear. A semi-Markov process is employed to describe the encountered failures of the actuator. By applying the Lyapunov–Krasovskii method, in combination with some novel inequalities, some conditions on the performance analysis are established, where some negative quadratic terms are fully considered to reduce the conservatism. Based on the conditions, an explicit expression for the desired controller is given. Three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the problem of robust [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust stabilization for Markovian jump delayed systems with partially known transition rates subject to input saturation. The problem we address is the design of dynamic anti-windup compensators, which guarantee that the resulting closed-loop constrained systems are robustly mean-square stable. By employing local sector conditions and an appropriate Lyapunov-Krasovskii function, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method. [ABSTRACT FROM AUTHOR]

• A co-design control approach under adaptive ETCS is developed to dispose of the stability problem for DPSs with spatial dimensions at the first attempt. • A comprehensive model is studied in this paper. • A novel ETCS with adaptive threshold parameters is put forward. This paper focuses on the problem of adaptive event-triggered L 2 − L ∞ control for distributed parameter systems with semi-Markov jump parameters. An event-triggered transmission scheme, whose threshold function can be adaptively adjusted, is established to decrease the frequency of data transmission. Simultaneously, the utilization of limited network bandwidth resources is also improved due to plenty of "unnecessary" packets being discarded before accessing networks. Furthermore, the jumping of stochastic parameters in networks can be described by a semi-Markov jump model, in which the sojourn-time is considered subject to the Weibull distribution instead of the exponential distribution. Based on the aforesaid discussions, a mode-dependent controller is designed under an adaptive event-triggered scheme. Whereafter, some criteria are constructed based on the Lyapunov stability theory to guarantee stochastic stability and a prescribed L 2 − L ∞ performance of the system. Ultimately, two simulation examples are provided to verify the feasibility of the proposed design approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite-time H ∞ control for Markov jump repeated scalar nonlinear systems (MJRSNSs) with input constraints. The jumps between MJRSNSs and desired mode-dependent controllers are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the different degrees of asynchronous jumps between MJRSNSs and controllers. With the aid of Lyapunov–Krasovskii methodology, some H ∞ performance criteria for the MJRSNSs are proposed. Based on these criteria, sufficient conditions on the existence of the desired controllers are established, and then the gains of the controllers can be obtained by solving a convex optimization problem. Finally, an example is presented to illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dissipativity-based filtering problem for a class of discrete-time Markov jump systems with mode-dependent time-varying delays and random packet losses. The phenomenon of packet losses occurs between the plant and the filter, which is characterized by introducing a random variable. Based on the single exponential smoothing method, the prediction of the missing measurement is used as the packet loss compensation when a packet is lost. Then, a partially mode-dependent filter is established in view of the fact that the mode signals of the original system may not be completely accessible to the filter. By employing a mode-dependent Lyapunov-Krasovskii functional, some novel sufficient conditions are obtained and the filter parameters are derived to ensure that the filtering error system is stochastically stable with a strictly (U , V , W)- γ -dissipative performance. Finally, a numerical example is utilized to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]