AQM scheme design for TCP network via Takagi‐Sugeno fuzzy method

This paper proposes a novel T‐S fuzzy control method instead of the traditional linear system control method to improve the TCP network performance. Thus a TCP network can be modeled as a T‐S fuzzy system, and by use of linear matrix inequality method and cone complementarity linearization algorithm, a fuzzy state feedback controller is provided while considering the problem of the asynchronous membership grades between the controller and the plant. Simulation results are presented to show that the proposed control approach can guarantee the asymptotical stability of the studied system and the desired queue size. © 2016 Wiley Periodicals, Inc. Complexity 21: 606–612, 2016     

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite‐time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well‐known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–19, 2016     

Fuzzy guaranteed cost output tracking control for fuzzy discrete‐time systems with different premise variables

This article investigates the problem of output tracking control for a class of discrete‐time interval type‐2 (IT2) fuzzy systems subject to mismatched premise variables. Based on the IT2 Takagi–Sugeno (T–S) fuzzy model, the criterion to design the desired controller is obtained, which guarantees the closed‐loop system to be asymptotically stable and satisfies the predefined cost function. Moreover, the controller to be designed does not need to share the same premise variables of the system, which enhances the flexibility of controller design and reduces the conservativeness. Finally, two examples are provided to demonstrate the effectiveness of the method proposed in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 265–276, 2016     

Robust stability of uncertain impulsive dynamical systems

This paper studies robust stability of uncertain impulsive dynamical systems. By introducing the concepts of uniformly positive definite matrix functions and Hamilton–Jacobi/Riccati inequalities, several criteria on robust stability, robust asymptotic stability and robust exponential stability are established. An example is also worked through to illustrate our results.     

Finite-time stability and controller design for a class of hybrid dynamical systems with deviating argument

This paper studies the finite-time stability (FTS) for a class of hybrid dynamical systems with deviating argument. An improved hybrid control scheme including sampled-data control as well as impulsive control is presented. Based on the theory of differential equations with piecewise constant argument of generalized type (PCAG) and the method of average impulsive interval (AII), several Lyapunov-based sufficient criteria for FTS are obtained in terms of linear matrix inequalities (LMIs), which can be verified via Matlab. The hybrid controller, in which the sampling instants could be different from the impulse instants, is designed by the established LMIs. The results in present paper are more convenient for application and less conservative than some existing ones. Finally, an example is given to illustrate the effectiveness and advantage of the obtained results.     

Exponential stability criterion for time-delay systems with nonlinear uncertainties

Exponential stability of time-delay systems with nonlinear uncertainties is studied in this paper. Based on the Lyapunov method and the approaches of decomposing the matrix, a new exponential stability criterion is derived in terms of a matrix inequality, which allows to compute simultaneously the two bounds that characterize the exponential nature of the solution. Some numerical examples are also given to show the superiority of our result to those in the literature.     

Robust exponential stabilization for large-scale uncertain impulsive systems with coupling time-delays

In this paper, we aim to study robust exponential stabilization for a large-scale uncertain impulsive system with coupling time-delays. Furthermore, we also provide an estimation of the rate of convergence of exponential stabilization. By utilizing the Lyapunov method and Razumikhin technique, we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed-loop large-scale uncertain impulsive system with coupling time-delays. Moreover, we shall also use the results obtained to design impulsive controllers for a large-scale uncertain continuous system under which the closed-loop continuous system achieves robust and exponential stability. To illustrate our results, one example is solved.     

Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.     

LMI criteria for robust chaos synchronization of a class of chaotic systems

Based on the Lyapunov stability theory and LMI technique, a new sufficient criterion, formulated in the LMI form, is established in this paper for chaos robust synchronization by linear-state-feedback approach for a class of uncertain chaotic systems with different parameters perturbation and different external disturbances on both master system and slave system. The new sufficient criterion can guarantee that the slave system will robustly synchronize to the master system at an exponential convergence rate. Meanwhile, we also provide a criterion to find out proper feedback gain matrix K$K$ that is still a pending problem in literature [H. Zhang, X.K. Ma, Synchronization of uncertain chaotic systems with parameters perturbation via active control, Chaos, Solitons and Fractals 21 (2004) 39–47]. Finally, the effectiveness of the two criteria proposed herein is verified and illustrated by the chaotic Murali–Lakshmanan–Chua system and Lorenz systems, respectively.     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Novel robust stability criteria for uncertain systems with time-varying delay

This paper is concerned with the delay-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. Through constructing a general form of Lyapunov–Krasovskii functional, and using integral inequalities, some slack matrices and newly established convex combination condition in the calculation, the delay-dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the improvement on the conservatism of the delay bound over some reported results in the literature.     

Synchronization of coupled chaotic FitzHugh-Nagumo systems

This paper addresses dynamic synchronization of two FitzHugh-Nagumo (FHN) systems coupled with gap junctions. All the states of the coupled chaotic system, treating either as single-input or two-input control system, are synchronized by stabilizing their error dynamics, using simplest and locally robust control laws. The local asymptotic stability, chosen by utilizing the local Lipschitz nonlinear property of the model to address additionally the non-failure of the achieved synchronization, is ensured by formulating the matrix inequalities on the basis of Lyapunov stability theory. In the presence of disturbances, it ensures the local uniform ultimate boundedness. Furthermore, the robustness of the proposed methods is ensured against bounded disturbances besides providing the upper bound on disturbances. To the best of our knowledge, this is the computationally simplest solution for synchronization of coupled FHN modeled systems along with unique advantages of less conservative local asymptotic stability of synchronization errors with robustness. Numerical simulations are carried out to successfully validate the proposed control strategies.     

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach

In this paper, an adaptive sliding mode controller for a novel class of fractional-order chaotic systems with uncertainty and external disturbance is proposed to realize chaos control. The bounds of the uncertainty and external disturbance are assumed to be unknown. Appropriate adaptive laws are designed to tackle the uncertainty and external disturbance. In the adaptive sliding mode control (ASMC) strategy, fractional-order derivative is introduced to obtain a novel sliding surface. The adaptive sliding mode controller is shown to guarantee asymptotical stability of the considered fractional-order chaotic systems in the presence of uncertainty and external disturbance. Some numerical simulations demonstrate the effectiveness of the proposed ASMC scheme.     

Robust chaos suppression for the family of nonlinear chaotic systems with noise perturbation

This paper investigates the robust chaos suppression problem for some classical Rössler systems using the sliding mode controller (SMC). Based on the proportional-integral (PI) switching surface, a SMC is derived to not only guarantee asymptotical stability of the equilibrium points of the Rössler systems but also reduce the effect of noise perturbation to an _H∞$H_{\infty }$-norm performance. The parameter matrix necessary for constructing both PI switching surface and the SMC can be easily solved by the linear matrix inequality (LMI) optimization technique. Finally, two illustrative examples are provided to demonstrate the efficacy of the proposed control methodology.