Some new algebraic criteria for chaos synchronization of Chua's circuits by linear state error feedback control

Abstract

SUMMARYThe research on the su cient criterion for chaos synchronization of the master-slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master-slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria.

Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

“…[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], some of which [5][6][7][8][9][10][11][12][13][14] proposed a few of sufficient synchronization criteria which depend on both the trajectories of the master system and that of the controlled slave system. However it is actually impossible to explicitly know the trajectory of the controlled slave system prior to the achievement of the synchronization.…”

“…Accordingly, a theoretical advance to be expected is to obtain global synchronization criterion independent of the trajectory of the slave system. Some literatures [18][19][20][21][22] have been devoted to deriving such a global synchronization criterion for the autonomous systems. Recently, some global synchronization criteria for the non-autonomous chaotic horizontal platform system with the trigonometric non-linear terms have been proposed [23].…”

“…In the past years, linear state error feedback control has been widely used to synchronize the chaotic systems and verified experimentally and numerically to be a simple and robust control technique applicable to chaos synchronization [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

CFAR detection of weak target in clutter using chaos synchronization

“…As shown in Figure 1, the received signal r (t) and the estimated clutter processĉ(t) are introduced to the two chaotic systems as external additive signals. To make the presentation clearer, traditional Chua's circuits [30][31][32] are used to realize the synchronization for target detection in the present study. However, it should be stressed that other chaotic systems can also be used for this detection application.…”

Real‐time chaotic circuit stabilization via inverse optimal control

“…In many areas such as telecommunications, electronics, Internet technology, chemical processes, biomedical systems, and so on, real-time chaos control is required, for which different techniques have been proposed to achieve chaos control; for instance, linear state feedback [1], Lyapunov function methods [2], adaptive control [3], and bang-bang control [4], among many others [5,6].…”