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This work investigates the observer-based asynchronous control of discrete-time nonlinear systems with network-induced communication constraints. To avoid the data collisions and side effects in a constrained communication channel, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is proposed. In contrast to the existing protocols, the DEWTOD scheduling regulates whether the sampling instant to release and which node to transmit the sampling instant simultaneously. In light of a hidden Markov model, the time-varying detection probability matrix is characterized by a polytopic set. By resorting to the polytopic-structured Lyapunov functional, sufficient conditions are derived such that the closed-loop dynamic is mean-square exponentially stable, and the observer-based controller is designed. In the end, two numerical examples are provided to explicate the validity of the attained methodology. [ABSTRACT FROM AUTHOR]

This brief is devoted to protocol-based control method design for semi-Markov switching systems with dynamic quantization. Essential different from the semi-Markov process with arbitrary switchings, by proposing a novel semi-Markov process subjected to a deterministic switching signal, a generalized framework of semi-Markov switching systems is set up. With respect to the quantization range of the dynamic quantizer, an improved event-triggered protocol associated with the quantizer parameter is proposed. On account of mode-dependent Lyapunov theory, sufficient conditions are established to ensure the stochastic finite-time boundedness of the resulting system. In the end, a tunnel diode circuit model shows the practicability and effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

This work is concerned with the issue of finite-time filter design for a type of Takagi–Sugeno (T–S) fuzzy Markov switching system (MSSs) with deception attacks (DAs). In view of communication network security, the randomly occurring DAs are considered in the measurement output (MO), in which the malicious unknown but bounded signals are launched by the adversary. Notably, to characterize the fallibility of the communication links between the MO and the filter, the packet dropouts, DAs, and quantization effects are taken into account simultaneously, which signifies that the resulting system is much more applicable than the existing results. Meanwhile, to deal with the phenomenon of asynchronous switching, a hierarchical structure approach is adopted, which involves the existing nonsynchronous/synchronous strategy as special cases. By means of a fuzzy-basis-dependent Lyapunov strategy, sufficient criteria are formulated such that the resulting system is stochastic finite-time boundedness under randomly occurring DAs. Finally, a double-inverted pendulum model and a numerical example are provided to validate the feasibility of the attained method. [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]

In this article, the issue of positive $\mathcal {L}_{1}$ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T–S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T–S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with $\mathcal {L}_{1}$ performance. Some solvability conditions for positive $\mathcal {L}_{1}$ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings. [ABSTRACT FROM AUTHOR]

This article focuses on static output feedback control for fuzzy Markovian switching singularly perturbed systems (FMSSPSs) with deception attacks and asynchronous quantized measurement output. Different from the previous work, both the logarithmic quantizer and the static output feedback controller are dependent on the operation system; by means of hidden Markov models, their modes run asynchronously with that of FMSSPSs. Additionally, the deception attacks are guided by a Bernoulli variable, and nonlinear characteristics are modeled by the Takagi–Sugeno fuzzy model. By resorting to a mode-dependent Lyapunov functional, several criteria are acquired and strictly $(\mathscr {Q},\mathscr {S},\mathscr {R})\text{--}\gamma$ -dissipative of FMSSPSs can be ensured. Finally, a dc motor model is expressed to illustrate the effectiveness of the asynchronous control scheme. [ABSTRACT FROM AUTHOR]

This brief is concerned with the mode-dependent sliding mode control (SMC) for uncertain discrete-time semi-Markov switching systems (S-MSSs). The switching is governed by a semi-Markov chain with a discrete-time semi-Markov kernel (SMK). First, a sliding mode surface (SMS) is constructed to be related to the current switching mode. Second, by means of the upper bound of the sojourn time (ST), some feasible conditions are derived to guarantee $\sigma $ -error mean square stability for the corresponding S-MSSs. Third, an appropriate SMC law is established to drive the state onto the specified sliding domain. Finally, an F-404 aircraft model validates the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This article is devoted to the fuzzy fault-tolerant tracking control of Markov jump systems with unknown mismatched faults. To reconstruct the faults and system states, a sequence of proportional–integral observers are established via the system outputs. With the help of a structure separation technique, the proportional–integral gains and the observer gains are solved by a unified linear matrix inequality framework. Resorting to the rebuilt faults and states from an iterative estimation algorithm, a backstepping-based fuzzy fault-tolerant tracking control scheme against the mismatched faults is established to make the resultant closed-loop system be uniformly ultimately bounded. Simulations are provided to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article investigates a spatial- $\mathcal {L}^{\infty }$ -norm-based reliable bounded control problem for a class of nonlinear partial differential equation systems in a finite-time interval. The main novelties are reflected in the following aspects: 1) inspired by the sector-nonlinearity approach, the considered nonlinear system is reconstructed by a Takagi–Sugeno fuzzy model, which provides an effective method for control design. Besides, several actuator failures, such as stuck faulty, outage faulty, and bias faulty, are taken into account and modeled by a novel Markov process; 2) partial areas’ states are sampled and transmitted based on a new distributed event-triggered communication strategy, which reduces the cost of the system design and saves the limited network resources to some extent; and 3) on the basis of the first two works, a new piecewise fuzzy controller, which requires fewer actuators compared with the distributed control method, is constructed. Then, some sufficient conditions to guarantee the finite-time boundedness (in the sense of spatial $\mathcal {L}^{\infty }$ norm) and mixed $\mathcal {L}_{2}-\mathcal {L}_{\infty }/\mathcal {H}_{\infty }$ disturbance attenuation performance are established, and a new linear matrix inequality relax technique is introduced to deal with the strict constraint that is caused by the asynchronous phenomenon between plant and controller. Finally, two simulation studies are given to illustrate the effectiveness and advantages of the developed controller. [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]

In this article, an investigation about the issue of fuzzy event-triggered asynchronous dissipative control for T–S fuzzy Markov jump systems (FMJSs) with unknown transition probabilities and nonuniform sampling is conducted. First of all, a mode-dependent looped Lyapunov–Krasovskii functional (LKF) is proposed, which takes full use of the available information not only from sawtooth structure characteristics but also from the inner sampling dynamics. Meanwhile, a hidden Markov chain is employed to depict the mismatch between the original system and the state-dependent fuzzy event-triggered controller. Then, based on the LKF methodology, matrix inequality techniques, and the reciprocally convex combination protocol, some relaxed criteria with respect to the stochastic stable of the considered system and the desired dissipative performance are derived, simultaneously. A numerical experiment is given to illustrate the significance of the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the stability of random impulsive delay differential systems with the kind of random impulsive intensity determined by an arbitrary random sequence or an irreducible aperiodic Markov chain. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second‐order moment processes. Based on the approaches of average impulsive interval and mode‐dependent average impulsive interval, the criteria of global asymptotic stability in probability and exponential stability in mth moment are constructed, respectively. In the end, the feasibility of the proposed theoretical results is verified by an example. [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]

This paper is concerned with the asynchronous fault detection and isolation (FDI) strategy in finite frequency domain for Markov jump systems (MJSs) with actuator failures under networked environment. A set of binary-valued Bernoulli distributed sequences is introduced to describe the transmission and the scheduling of the sensor nodes. Then, an MJS directing by two Markov process and with multiple stochastic parameters is derived to characterize the whole system dynamics. Subsequently, by means of the stochastic $\mathcal {H}_{-}$ index in finite frequency domain and the geometric mapping approach, an asynchronous FDI scheme is investigated, in which the filters complete the FDI mission with only partial information of the measurements. Meanwhile, each FDI filter is only sensitive to one possible actuator fault and decoupled from others. Then the existence of the desired filters is ensured by some novel sufficient conditions. Finally, an application example is presented to show the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This article concentrates on the nonstationary control for a class of nonlinear Markovian switching systems (MSSs) with the Tagaki–Sugeno (T–S) fuzzy model. By adopting variable quantization density, a more general type of T–S fuzzy MSSs is established, in which the varies performance demands can be satisfied in a more flexible way. The major benefit of the developed method lies that a multiple hierarchical structure strategy is developed concerning nonsynchronization among the original system, controller, and quantizer, which covers the reported asynchronous/synchronous mechanisms as special cases. On the basis of fuzzy-basis-dependent and mode-dependent Lyapunov function, some sufficient conditions are derived and controller gains are designed. Finally, the feasibility of the achieved result is verified by a practical example. [ABSTRACT FROM AUTHOR]

This article addresses the issue of asynchronous partially mode-dependent filtering for networked Markov switching repeated scalar nonlinear systems (MSRSNSs) subject to quantized measurements (QMs). Especially, a novel partially mode-dependent filter (PMDF) is constructed, where the signal transmission of a filter mode occurred randomly and is modeled by a Bernoulli distributed sequence. The designed PMDF is different from state mode, which is governed by an asynchronous switching rule. By utilizing a diagonally dominant-type Lyapunov functional (DDTLF), sufficient conditions ensure that the existence of the PMDF and the $l_{2}-l_{\infty }$ performance index are derived. Finally, an economic example is adopted to substantiate the applicability of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the reliable extended passive control problem for semi-Markov jump Takagi-Sugeno (T–S) fuzzy systems based on an event-triggered mechanism (ETM). An asynchronous approach is utilized to cope with the fuzzy-basis-dependent membership functions in networked fuzzy systems. For fear of the waste of communication resources, an ETM to screen the transmitted data is adopted for T–S fuzzy semi-Markov jump systems under consideration. Owing to the use of Lyapunov stability theory and some novel integral inequalities based on auxiliary functions, some sufficient conditions are obtained to guarantee that the resulting closed-loop system not only meets a prescribed mixed $\mathcal {H} _{\infty }$ and passive performance but also is stochastically stable. Then, by using a skillful matrix decoupling approach, the gains of the fuzzy controller may be expressed specifically. Lastly, the superiority and availability of the developed design method are extensively described and validated via its application to a truck control model. [ABSTRACT FROM AUTHOR]

In this article, a method to design the filter for fuzzy jumping genetic regulatory networks is explored. The case when the filters cannot directly utilize the mode information of the plant is taken into account. A hidden Markov model is introduced to address such a problem. Furthermore, a mature scheduling method, namely round-robin protocol, is employed to optimize the data transmission in genetic regulatory networks. On the basis of the fuzzy model approach and the stochastic analysis technique, some novel conditions ensuring the H∞ performance and stochastic stability of the error system are established. The parameters of the filter can be presented via addressing the convex optimization problem. The feasibility of results is finally illustrated by considering a repressilator model subject to stochastic jumping parameters. [ABSTRACT FROM AUTHOR]

In the study, the authors are interested in investigating the stability analysis and state estimation of Markov jump static neural networks subject to time delays by the feat of Bessel–Legendre inequality. A canonical Bessel–Legendre inequality, which converts the limited interval [−h,0] required in traditional Bessel–Legendre inequality to a general interval [a,b] is employed. Accordingly, compared with the existing results, the restriction is naturally relaxed and the less conservative criterion is presented. The stability analysis is complicated after constructing an enhanced Lyapunov–Krasovskii functional suitable for the canonical Bessel–Legendre inequality. Furthermore, taking account of the information of system mode, the mode‐dependent scheme is applied to the design of a state estimator. Corresponding results to the stability of the estimation error system and the acquisition of the desired observer are presented. In the end, an example, which proves the validity of the method is given. [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]

This paper is concerned with the fuzzy-model-based nonfragile control problem for discrete-time nonlinear singularly perturbed systems with stochastic jumping parameters. The stochastic parameters are generated from the semi-Markov process. The memory property of the transition probabilities among subsystems is fully considered in the investigated systems. Consequently, the restriction that the transition probabilities are memoryless in widely used discrete-time Markov jump model can be removed. Based on the T-S fuzzy model approach and semi-Markov kernel concept, several criteria ensuring $\delta$ -error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the designed procedures which could well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller are presented. A technique is developed to estimate the permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-triggered nonfragile H ∞ filtering of Markov jump systems with interval variations. Integrating the sampler failure into the filter design, two independent random variables satisfying the Bernoulli distribution are utilized to describe the imperfect transmissions from sensor to event generator and event generator to filter, respectively. The resultant event-triggered scheme is represented by a stochastic form. With the help of stochastic analysis technique, sufficient conditions for the filtering error system to be stochastically stable with the required H ∞ performance are formulated in terms of linear matrix inequalities. A structured vertex separation method is adopted to handle filter gains with interval variations. The validity of the proposed approach is verified by an RLC circuit. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of event-triggered control for a class of fuzzy Markov jump systems with general switching policies. A novel event-triggered scheme is proposed to improve the transmission efficiency at each sampling instance. Each transition rate allows to be unknown, known, or only its uncertain domains value is known. With the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller, sufficient conditions for the resulting fuzzy Markovian jump systems are established in terms of coupled linear matrix inequalities. Finally, an example is given to illustrate the validity of the developed technique. [ABSTRACT FROM PUBLISHER]

This study is concerned about the quantitative exponential stability (QES) and stabilisation of discrete‐time Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finite‐time stability (GFTS), the relations among QES, GFTS and finite‐time stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observer‐based controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results. [ABSTRACT FROM AUTHOR]

This paper addresses a fault detection strategy in finite frequency domain for networked system with communication constraints and packet loss. The considered communication constraint is that only one data packet can gain into the networks at each time-slot, and the fault detection filters complete the task with only partially available measurements. With consideration of the data packet loss and the stochastic scheduling protocol, a nonhomogeneous Markov jump system is firstly derived to describe the networked systems. For this class of systems, the generalized Kalman-Yakubovic-Popov lemma-based finite frequency fault detection filter design methods are invalid. To tackle this problem, a new mode-dependent lemma is developed to capture the system performance in finite frequency domain. Further, a set of fault detection filters are designed corresponding to the accessed nodes accordingly. Finally, an example is given to show the effectiveness of the proposed fault detection approach. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This study investigates the sampled‐data reliable control for a class of Takagi‐Sugeno (T‐S) fuzzy semi‐Markovian jump system (FSMJS). The system under consideration involves semi‐Markov stochastic process that is described by the property of cumulative distribution function. To relax the difficulty of finding upper bounds in sample‐and‐hold behaviour of the FSMJS, a novel method named mismatched membership function is presented. Sufficient conditions that can guarantee the T–S FSMJS to be stochastically stable are given. More precisely, the reliable sampled‐data controller is designed in terms of linear matrix inequalities. Finally, the validity of the presented approach is demonstrated by a controller design for a single‐link robot arm model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite-time asynchronous [ABSTRACT FROM AUTHOR]

This paper addresses the dynamic output feedback control issue for nonhomogeneous Markov switching systems with an event-triggered round-robin protocol. The transition probability matrix of the nonhomogeneous Markov process is time-varying, which can be characterized by a polytopic structure. To alleviate the communication burden in a shared network, as a first effort, a novel dynamic event-triggered round-robin protocol is forwarded to regulate whether to release the measurements and which ones to release. In light of the dynamic event-triggered round-robin protocol, an asynchronous dynamic output feedback control law is constructed, which reflects the mismatching phenomenon of modes switching between the nonhomogeneous Markov switching systems and the desired controllers. By resorting to a novel Lyapunov functional, sufficient conditions are attained to guarantee the stochastic stability of the augmented dynamic. At last, two examples are addressed to verify the effectiveness and applicability of the theoretic results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the control of Markov jump nonlinear systems with general transition probabilities (TPs) allowed to be known, uncertain, and unknown. With the help of the S-procedure to dispose the system nonlinearities and the TP property to eliminate the coupling between unknown TP and Lyapunov variable, an extended bounded real lemma for the considered system to be stochastically stable with the prescribed \mathcal H{\infty } performance is established in the framework of linear matrix inequalities. To handle the nonlinearity incurred by uncertain TP for controller synthesis, a separated method is proposed to decouple the interconnection between Lyapunov variables and controller gains. A numerical example is given to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper addresses the H ∞ filtering of continuous Markov jump linear systems with general transition probabilities and output quantization. S-procedure is employed to handle the adverse influence of the quantization and a new approach is developed to conquer the nonlinearity induced by uncertain and unknown transition probabilities. Then, sufficient conditions are presented to ensure the filtering error system to be stochastically stable with the prescribed performance requirement. Without specified structure imposed on introduced slack variables, a flexible filter design method is established in terms of linear matrix inequalities. The effectiveness of the proposed method is validated by a numerical example. [ABSTRACT FROM AUTHOR]

This study addresses the estimation problem for discrete‐time measurement‐delay systems with multiplicative noise and Markov jump. First, the state equation is converted into two equations according to the geometric arguments and flexible transformations. Then, based on the reorganised innovation approach, the finite‐horizon linear minimum mean‐square‐error estimator is derived in terms of two Riccati difference equations and two Lyapunov difference equations. Finally, under the assumptions of mean square stability of the system and ergodicity of the associated Markov chain, a sufficient condition for the existence of the infinite‐horizon estimator is presented. We provide a numerical example to manifest the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the reliable mixed passive and [ABSTRACT FROM AUTHOR]

In this paper, the stochastic admissibility analysis problem is investigated for a class of singular Markov jump delayed systems (SMJDSs). The purpose is to establish some conditions such that the SMJDSs are stochastically admissible and strictly ( X , Y , Z )- μ -dissipative. A mode-dependent Lyapunov functional and some novel inequalities are proposed for the considered SMJDSs. Based on these, some new stochastic admissibility conditions are established. In comparison with the existing results, the advantage of the obtained conditions lies in the fact that they are not only less conservatism but also more general. Four numerical examples borrowed from some existing papers are given to demonstrate the effectiveness and the reduced conservatism of the presented method. [ABSTRACT FROM AUTHOR]

This study is concerned with the non‐fragile mixed ℋ∞ /l2 − l∞ synchronisation control problem for discrete‐time complex networks with Markov jumping‐switching topology under unreliable communication links. The network topology under consideration is assumed to be governed by a Markov chain with time‐varying transition probabilities (TPs). The variation of TPs is subject to a kind of slow switching signals; that is, the average dwell time (ADT) switching. The focus is on the design of non‐fragile mixed mode‐dependent/‐independent controllers such that the underlying network reaches stochastic mean‐square synchronisation with a mixed ℋ∞ /l2 − l∞ performance level for an admissible switching signal with ADT. By using a new mixed ℋ∞ /l2 − l∞ performance index, combined with the switched control method, the solutions to the considered problem are formulated. Finally, simulation results demonstrate the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

This study is concerned with the finite‐time energy‐to‐peak filtering problem for Markov jump repeated scalar non‐linear systems with packet dropouts. The packet dropout phenomenon occurs in a random way and is modelled by a stochastic variable satisfying the Bernoulli distribution. The purpose of the study is to design a filter such that the resulting filtering error system is stochastically finite‐time bounded, and a prescribed energy‐to‐peak performance level is achieved over a finite time interval. By using the mode‐dependent diagonally dominant Lyapunov function approach, some strict linear matrix inequality‐based conditions are established for the existence of an admissible filter, and a corresponding explicit parameterisation of such a filter is obtained. Finally, a numerical example with simulation is presented to demonstrate the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the problem of mixed and passive filter design for Markovian jump impulsive networked control systems with norm bounded uncertainties and random packet dropouts. The system under consideration is modeled by means of an impulsive subsystem, and the network-induced imperfections like packet dropout and delay are described by a Bernoulli distributed white sequence. The delay in the model is assumed to be time-varying. The mode-dependent conditions are established to guarantee the filtering error system to be robustly stochastically stable and achieve a prescribed mixed and passivity performance index. The sufficient conditions for the existence of admissible filters are expressed by using the linear matrix inequality (LMI) approach and convex optimization problem. The corresponding filter parameters can be obtained by solving the set of LMIs, which can be easily facilitated by using some standard numerical packages. Finally, a numerical example is given to illustrate the effectiveness and potential of the proposed filter design. [Copyright &y& Elsevier]

This study deals with the problem of finite‐time reliable ℒ2 − ℒ∞ /ℋ∞ control for non‐linear systems with actuator faults through Takagi–Sugeno fuzzy model approach. The actuator failure model under consideration is assumed to be governed by a homogenous Markov chain. The focus is on the design of a fuzzy Markov switching fault‐tolerant controller such that the resulting closed‐loop system is stochastically finite‐time bounded with a mixed ℒ2 − ℒ∞ /ℋ∞ performance level over a finite‐time interval. Some sufficient conditions for the solvability of the above problem are given in terms of linear matrix inequalities by introducing a new mixed ℒ2 − ℒ∞ /ℋ∞ performance function. Finally, a quarter‐vehicle suspension model is employed to demonstrate the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with a delay-dependent state estimator for neutral-type neural networks with mixed time-varying delays and Markovian jumping parameters. The addressed neural networks have a finite number of modes, and the modes may jump from one to another according to a Markov process. By construction of a suitable Lyapunov- Krasovskii functional, a delay-dependent condition is developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable in a mean square. The criterion is formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. [ABSTRACT FROM AUTHOR]

This study analyzes the problem of hidden Markov model based control for periodic systems subject to singular perturbations and Lur'e cone-bounded nonlinearity. Different from the existing time-invariant fading channels, the fading channels are alleviated to be time-varying. Furthermore, to better depict the time-varying property of the fading channels, a novel periodic Markov process framework subject to mean and variance is developed. The highlight of this study lies that the hidden Markov model detector is forwarded to observe the fading channel mode, whose detection probabilities are generalized to be partially recognized. New techniques are developed in dealing with the stochastic Lyapunov functional, and sufficient conditions are gained to ensure the resulting dynamic is stochastically stable. In the sequel, the asynchronous controller parameters are further achieved to reflect the discrepancy between fading channel mode and its detected one. Finally, an application-oriented example is rendered to confirm the effectiveness and applicability of the developed control strategy. [ABSTRACT FROM AUTHOR]