Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

Delay‐dependent robust reliable control for uncertain switched neutral systems

This article investigates the robust reliable control problem for a class of uncertain switched neutral systems with mixed interval time‐varying delays. The system under study involves state time‐delay, parameter uncertainties and possible actuator failures. In particular, the parameter uncertainties is assumed to satisfy linear fractional transformation formulation and the involved state delay are assumed to be randomly time varying which is modeled by introducing Bernoulli distributed sequences. The main objective of this article is to obtain robust reliable feedback controller design to achieve the exponential stability of the closed‐loop system in the presence of for all admissible parameter uncertainties. The proposed results not only applicable for the normal operating case of the system, but also in the presence of certain actuator failures. By constructing an appropriate Lyapunov–Krasovskii functional, a new set of criteria is derived for ensuring the robust exponential stability of the closed‐loop switched neutral system. More precisely, zero inequality approach, Wirtinger's based inequality, convex combination technique and average dwell time approach are used to simplify the derivation in the main results. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the proposed design approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–237, 2016     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

Robust Stability Criterion for Discrete‐Time Nonlinear Switched Systems with Randomly Occurring Delays via T–S Fuzzy Approach

This article investigates exponential stability of uncertain discrete‐time nonlinear switched systems with parameter uncertainties and randomly occurring delays via Takagi–Sugeno fuzzy approach. The randomness of time‐varying delay is characterized by introducing a Bernoulli stochastic variable that follows certain probability distribution. By adopting the average dwell‐time approach with Lyapunov–Krasovskii functional and using convex reciprocal lemma, delay‐dependent sufficient conditions for exponential stability of the switched fuzzy system are derived in terms of linear matrix inequalities (LMIs), which can be solved readily using any LMI solvers. Finally, illustrative examples are provided to demonstrate the effectiveness of the proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 20: 49–61, 2015     

Mean square exponential synchronization for impulsive coupled neural networks with time‐varying delays and stochastic disturbances

In this article, the mean square exponential synchronization of a class of impulsive coupled neural networks with time‐varying delays and stochastic disturbances is investigated. The information transmission among the systems can be directed and lagged, that is, the coupling matrices are not needed to be symmetrical and there exist interconnection delays. The dynamical behaviors of the networks can be both continuous and discrete. Specially, the time‐varying delays are taken into consideration to describe the impulsive effects of the system. The control objective is that the trajectories of the salve system by designing suitable control schemes track the trajectories of the master system with impulsive effects. Consequently, sufficient criteria for guaranteeing the mean square exponential convergence of the two systems are obtained in view of Lyapunov stability theory, comparison principle, and mathematical induction. Finally, a numerical simulation is presented to show the verification of the main results in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 190–202, 2016     

Asymptotic synchronization of continuous/discrete complex dynamical networks by optimal partitioning method

The synchronization problem for both continuous and discrete‐time complex dynamical networks with time‐varying delays is investigated. Using optimal partitioning method, time‐varying delays are partitioned into l subintervals and generalized results are derived in terms of linear matrix inequalities (LMIs). New delay‐dependent synchronization criteria in terms of LMIs are derived by constructing appropriate Lyapunov–Krasovskii functional, reciprocally convex combination technique and some inequality techniques. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2014 Wiley Periodicals, Inc. Complexity 21: 193–210, 2015     

Chaos control of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity

This article presents an adaptive sliding mode control (SMC) scheme for the stabilization problem of uncertain time‐delay chaotic systems with input dead‐zone nonlinearity. The algorithm is based on SMC, adaptive control, and linear matrix inequality technique. Using Lyapunov stability theorem, the proposed control scheme guarantees the stability of overall closed‐loop uncertain time‐delay chaotic system with input dead‐zone nonlinearity. It is shown that the state trajectories converge to zero asymptotically in the presence of input dead‐zone nonlinearity, time‐delays, nonlinear real‐valued functions, parameter uncertainties, and external disturbances simultaneously. The selection of sliding surface and the design of control law are two important issues, which have been addressed. Moreover, the knowledge of upper bound of uncertainties is not required. The reaching phase and chattering phenomenon are eliminated. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 13–20, 2016     

Exponential state estimator design for discrete‐time neural networks with discrete and distributed time‐varying delays

In this article, the probl of state estimation for discrete‐time neural networks with mixed time‐varying delays is investigated. The mixed time delays consist of both discrete and distributed delays. An appropriate Lyapunov–Krasovskii functional put forward to reflect the mixed time‐varying delays is proposed to establish sufficient conditions for the existence of admissible state estimators. The conditions are described in the form of linear matrix inequalities (LMIs), which guarantee the estimation error to be globally exponentially stable in the presence of mixed time‐varying delays. Then, the desired estimator matrix gain can be characterized in terms of the solution to these LMIs. A numerical example is addressed to show the effectiveness of the proposed design method. © 2014 Wiley Periodicals, Inc. Complexity 20: 38–48, 2014     

Cluster synchronization for T–S fuzzy complex networks using pinning control with probabilistic time‐varying delays

In this article, cluster synchronization problem for Lur'e type Takagi–Sugeno (T–S) fuzzy complex networks with probabilistic time‐varying delays is considered. Pinning control strategy is proposed. The probability distribution of the time‐varying delay is considered. In terms of the probability distribution of the delays, a new type of system model with probability‐distribution‐dependent parameter matrices is proposed. Moreover, probabilistic delay is assumed to satisfy certain probability distribution and the probability of the delay takes values in some intervals. By constructing a suitable Lyapunov–Krasovskii functional involving triple integral terms and using Kronecker product with convex combination technique, some sufficient conditions are derived to ensure the cluster synchronization of designed networks such that the linear feedback controller can be used to every cluster. The problem of controller design is converted into solving a series of linear matrix inequalities. The effectiveness of our results is verified through numerical examples and simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–77, 2015     

Robust dissipativity and passivity analysis for discrete‐time stochastic neural networks with time‐varying delay

In this article, we consider the problem of robust dissipativity and passivity analysis for a class of general discrete‐time recurrent neural networks (NNs) with time‐varying delays. The NN under consideration is subject to time‐varying and norm bounded parameter uncertainties. By the latest free‐weighting matrix method, an appropriate Lyapunov–Krasovskii functional and using stochastic analysis technique a sufficient condition is established to ensure that the NNs under consideration is strictly ‐dissipative. The derived conditions are presented in terms of linear matrix inequalities. Numerical examples and its simulations are given to demonstrate the effectiveness of the results. © 2014 Wiley Periodicals, Inc. Complexity 21: 47–58, 2016     

Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 John Wiley & Sons, Ltd.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

Robust stability results for nonlinear Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties

This article is concerned with the robust stability analysis for Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties. Sufficient delay‐dependent stability results are derived with the help of stability theory and linear matrix inequality technique using direct delay‐decomposition approach. Here, the delay interval is decomposed into two subintervals using the tuning parameter η such that , and the sufficient stability conditions are derived for each subintervals. Further, the parameter uncertainties are assumed to be occurring in a random manner. Numerical examples are given to validate the derived theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 50–60, 2016     

Full‐Order observer design for nonlinear complex large‐scale systems with unknown time‐varying delayed interactions

This article is concerned with the problem of state observer for complex large‐scale systems with unknown time‐varying delayed interactions. The class of large‐scale interconnected systems under consideration is subjected to interval time‐varying delays and nonlinear perturbations. By introducing a set of argumented Lyapunov–Krasovskii functionals and using a new bounding estimation technique, novel delay‐dependent conditions for existence of state observers with guaranteed exponential stability are derived in terms of linear matrix inequalities (LMIs). In our design approach, the set of full‐order Luenberger‐type state observers are systematically derived via the use of an efficient LMI‐based algorithm. Numerical examples are given to illustrate the effectiveness of the result. © 2014 Wiley Periodicals, Inc. Complexity 21: 123–133, 2015     

Robust guaranteed cost control for discrete‐time systems via partially delay‐dependent controller with linear fractional uncertainties

In this article, a partially delay‐dependent controller is designed to analyze the guaranteed performance analysis of a class of uncertain discrete‐time systems with time‐varying delays. By constructing suitable Lyapunov–Krasovskii Functional (LKF), sufficient conditions are derived to ensure the system to be robustly stochastically stable in mean square sense by using Wirtinger‐based inequality and convex reciprocal lemma. The proper cost function is chosen to guarantee an adequate level of performance. The derived conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in MATLAB. Further, the advantage of employing the obtained results is illustrated via numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 113–122, 2016