Exponential synchronization of chaotic Lur'e systems with time-varying delay via sampled-data control

In this paper, we study the exponential synchronization of chaotic Lur＇e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov-Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequal- ities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

In this paper we present a synchronization method for chaotic Lur＇e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur＇e systems with deadzone nonlinearity. Based on the Lyapunov-Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality （LMI） formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.

Pinning control of complex Lur’e networks

This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Synchronization of general discrete Lur'e systems

This paper studies a master-slave type of synchronization systems for a general form of two discrete Lur＇e systems. Some simple necessary and/or sufficient conditions for synchronization are derived. They are basically algebraic conditions, and are convement to be applied in engineering applications.

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.

Analysing chaos in fractional-order systems with the harmonic balance method

In this paper, the fractional-order Genesio-Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.

Master-slave synchronization of singular Lur'e systems with time-delay

This paper is concerned with the problem of designing a time-delay output feedback control law for masterslave synchronization of singular Lur＇e systems. Using generalized Lyapunov stability theory, a sufficient condition for the existence of such feedback control law is given and an explicit expression of such control law is also achieved. These algorithms are formulated in terms of linear matrix inequalities, which can be easily performed numerically. A numerical example is used to illustrate the effectiveness of the design method.

Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems

The paper deals with the g2-stability analysis of multi-input-multi-output （MIMO） systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin- earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain. These conditions have the following features： i） They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block, ii） For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.