B. Kaviarasan

Synchronization and state estimation for stochastic complex networks with uncertain inner coupling

This paper addresses the synchronization and state estimation problems for an array of coupled discrete-time stochastic complex networks (SCNs) with uncertain inner couplings in which time-varying delay is considered both in the network couplings and dynamical nodes. In particular, the uncertainties encountering in coupling terms are characterized by using the interval matrix approach. By constructing a suitable LyapunovKrasovskii functional and utilizing Kronecker product properties, a new set of sufficient conditions is established in terms of linear matrix inequalities to guarantee the synchronization of the addressed SCNs with a prescribed mixed H and passivity performance index. Moreover, the state estimation problem is then studied for the same SCNs with uncertain inner coupling strength and subsequently, the estimator is designed. More precisely, Schur complement, discrete-time Jensens inequality together with reciprocally convex combination approach are used to simplify the derivations in the main results. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed synchronization and state estimation results.

Finite-time dissipative based fault-tolerant control of Takagi–Sugeno fuzzy systems in a network environment

Abstract This work deals with the problem of robust finite-time dissipativity based fault-tolerant controller design for a class of Takagi–Sugeno (T–S) fuzzy systems in a network environment against system uncertainties, external disturbances and nonlinear actuator failures. Specifically, an actuator fault model consisting both linear and nonlinear faults is developed during the reliable control design. By employing Lyapunov technique together with Wirtinger based integral inequalities, a new set of delay-dependent sufficient conditions is established which assures that the resulting closed-loop system is finite-time bounded and finite-time ( Q , S , R ) − μ dissipative. Based on the established sufficient conditions, the reliable control design parameters are determined by solving a set of linear matrix inequalities (LMIs). Moreover, the performances of H∞, sector bounded and mixed H∞ and passivity can be obtained as the special cases from the established result. In the end, two numerical examples, one of them is based on a mass-spring-damper system in a network environment, are presented to display the effectiveness, less conservativeness and advantage of the developed design technique.

Finite-time mixed H∞ and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

ABSTRACT This paper is concerned with the finite-time mixed H∞ and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixed H∞ and passive performance index is achieved. Moreover, the robust mixed H∞ and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unify H∞ and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique.

Reliable state estimation of switched neutral system with nonlinear actuator faults via sampled-data control

This paper aims to solve the reliable state estimation problem of an uncertain switched neutral system subject to nonlinear actuator faults and time-varying delay by using sampled-data approach. To be precise, the well-known Luenberger estimator is constructed to determine the immeasurable states of the addressed system and a general actuator fault model is employed to describe the nonlinearities encountering in the control design. After that, by defining an error variable, the corresponding estimation error system is formulated. By the virtue of Lyapunov–Krasovskii stability theory and average dwell-time method, a new delay-dependent sufficient criterion is established to guarantee the existence of the desired estimator and sampled-data gains and subsequently, the explicit expression of those gains is presented by means of the solution to a set of linear matrix inequalities. Moreover, two numerical examples are given to show the efficiency of the proposed estimator design schemes, where it is shown that the estimator gains can ensure the exponential stability of the considered switched neutral systems.

Non-fragile filtering for singular Markovian jump systems with missing measurements

Abstract In this paper, the issue of an non-fragile filter design is addressed for a class of discrete-time singular Markovian jump systems subject to time-varying delay and missing measurements based on the extended passivity theory. In particular, the missing probability is assumed to be affected by norm-bounded uncertainties. Moreover, the proposed filter design is more general and realistic since it unifies the mode-independent and mode-dependent characteristics in a single framework. By using Lyapunov–Krasovskii stability theory and Abel lemma, a new set of sufficient conditions is established which ensures the stochastic admissibility of the resulting error system with a prescribed disturbance attenuation level. Based on the sufficient conditions, the explicit expression of the desired filter gain matrices is formulated in terms of linear matrix inequalities. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed non-fragile filter design, wherein it is showed that the proposed method yields less conservative results over some existing methods.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

Abstract This article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

Resilient control design for consensus of nonlinear multi-agent systems with switching topology and randomly varying communication delays

Abstract This paper examines the robust consensus problem of nonlinear multi-agent systems via a resilient controller subject to switching topology, wherein the effect of uncertainty in the form of additive perturbations and a randomly varying communication delay is considered in the control design. In particular, a directed graph is used to describe the interaction topology of the addressed multi-agent system and a stochastic variable obeying the Bernoulli distributed white sequences is incorporated to represent the randomness of delay. By utilizing the Lyapunov’s direct method and some matrix operations, a sufficient condition for mean-square asymptotic consensus of the addressed system is derived. Subsequently, the explicit characterization of the resilient control gain is obtained by means of linear matrix inequalities that can be effectively solved by using the ideas of convex optimization. An academic example is eventually presented to illustrate the significance and potency of the proposed control design strategy.

Leader-following exponential consensus of input saturated stochastic multi-agent systems with Markov jump parameters

Abstract This paper is concerned with the solvability of leader-following exponential consensus of a stochastic nonlinear multi-agent system in the presence of Markov jump parameters and input saturation by using a fault-tolerant control scheme. Firstly, the interconnection topology that represents the communication between the leader and follower agents is chosen to be undirected and fixed. Secondly, to exhibit real scenario, a time-varying actuator fault model is incorporated in the fault-tolerant control design. Thirdly, by introducing a simple linear transformation, an error system is then formulated. Based on these setups and by employing the tools from algebraic graph theory and Lyapunov–Krasovskii stability theory, a distributed robust fault-tolerant controller is designed for each follower node in terms of linear matrix inequalities such that the closed-loop error system is exponentially stable in the sense of mean-square even in the presence of possible actuator faults. Lastly, a simulation study is presented to illustrate the efficacy of the proposed control design technique.

Resilient sampled-data control design for singular networked systems with random missing data

Abstract This paper proposes an active resilient control strategy for singular networked control systems with external disturbances and missing data scenario based on sampled-data scheme. To characterize the missing data scenario, a stochastic variable satisfying Bernoulli distributed white sequence is introduced. Based on this scenario, in this paper, two different models are proposed. For both the models, by using Lyapunov–Krasovskii functional approach, which fully uses the available information about the actual sampling pattern, some sufficient conditions in terms of linear matrix inequalities (LMIs) are separately obtained to guarantee that the resulting closed-loop system is admissible and strictly dissipative with a prescribed performance index. In particular, Jensen’s and Wirtinger based integral inequalities are employed to simplify the integral terms which appeared in the derivation of stabilization results. Then, if the obtained LMIs are feasible, the corresponding parameters of the designed resilient sampled-data controller are determined. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed control design technique.

Dissipativity-based non-fragile sampled-data control design of interval type-2 fuzzy systems subject to random delays

This paper investigates the β-dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov-Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly -β-dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique.