Impulsive Synchronization of Chaotic Systems via Linear Matrix Inequalities

Abstract

Impulsive synchronization of chaotic systems is studied in this paper. By exploring the structural knowledge of the systems and using linear matrix inequalities, some less conservative conditions than existing results are derived. With the new conditions, the bound of intervals for transmitting impulses can be increased and this results in higher bandwidth efficiency. Our results are thus able to improve the efficiencies of the existing technologies on chaotic secure communications and chaotic spread communications.

A Lie Algebraic Condition of Stability for Hybrid Systems and Application to Hybrid Synchronization

“…In , the authors utilized switched Lyapunov functions and control impulses in different models to obtain the stability of switching and impulsive systems as well as the synchronization of nonlinear systems. Nowadays, synchronization of nonlinear dynamics, such as chaotic dynamics, has been widely studied during the last few years because of its role in understanding the basic features of coupled nonlinear systems and in view of potential applications in communication systems, time series analysis and modeling [Chua et al, 1986;Ginoux & Rossetto, 2006;He et al, 2006;Ji et al, 2006;Li et al, 2004;Sun & Zhang, 2004;Wen et al, 2006].…”

Impulsive synchronization of chaotic Lur'e systems via partial states

“…In [2], the stability theory of impulsive differential equations [3] were first applied to design impulsive control law to synchronize two identical chaotic systems. Since then, impulsive control method for synchronization of chaotic systems have received increasing interests and a lot of research works have been accumulated, see [4][5][6][7][8][9][10][11][12][13][14]. The main idea of impulsive control method is to suppress the states of the system at discrete time instants.…”

“…The advantage of impulsive control scheme for synchronization of chaotic systems lies in that only the synchronization impulses are sent to the driven system at the impulsive instants, which can decrease the information redundancy in the transmitted signal and increase robustness against the disturbances. However, in the most existing impulsive synchronization results [2][3][4][5][6][7][8][9][10][11][12][13], the impulsive control input is always exerted on all the states of the driven system, which means that knowledge of the full state information of the driven system is needed. In practice, some states of the driven system are often not available, not measurable or too expensive to measure.…”

“…In practice, some states of the driven system are often not available, not measurable or too expensive to measure. Thus, the applications of those results in [2,[4][5][6][7][8][9][10][11][12][13] are limited. In [14], an impulsive control strategy via a single variable is proposed to synchronize two identical Chua's circuits.…”

Chaotic communication systems in the presence of parametric uncertainty and mismatch

“…A variety of schemes have been proposed to synchronize two chaotic systems, see, for example, [1][2][3][4][5][6][7][8]. These schemes are obtained under strong assumptions that the parameters of chaotic systems are time invariant and these parameters should be identical for both chaotic systems, in order to ensure perfect synchronization.…”