The stabilization and synchronization of Chua's oscillators via impulsive control

Abstract

Abstract-This paper considers the stabilization and synchronization of Chua's oscillators via an impulsive control with time-varying impulse intervals. Some less conservative conditions were derived in the sense that the Lyapunov function is only required to be nonincreasing along a subsequence of the switchings.

Stability of a Class of Hybrid Impulsive and Switching Systems

“…and more flexible design, to achieve stabilization than the individual single continuous control, discrete control, impulsive control, or switching control in (Li et al, 2001).…”

“…So far, most research work on hybrid systems has been devoted to stability analysis and stabilization, (Decarlo et al, 2000;Liberzon and Morse, 1999;Liberzon, 2003;Michel, 1999). Most recently, on the basis of Lyapunov functions and other analysis tools, the stability and stabilization for linear or nonlinear switched systems have been further investigated and many valuable results have been obtained (Daafouz et al, 2002;Ge et al, 2001;Ishii and Francis, 2002;Leonessa et al, 2001;Li et al, 2001;Mancilla-Aguilar, 2003), etc..…”

“…Hybrid systems consisting of interacting continuous and discrete dynamics under certain logic rules, have gained considerable attention in science and engineering (Aubin et al, 2001;Branicky, 1998;Decarlo et al, 2000;Ge et al, 2001;Hespanha and Morse, 1999;Li et al, 2001;Liberzon and Morse, 1999;Mancilla-Aguilar, 2003), since they provide a natural and convenient unified framework for mathematical modeling of many complex physical phenomena and practical applications. Examples include robotics, integrated circuit design, multi-media, manufac-turing, power electronics, switched-capacitor networks, chaos generators, automated highway systems and air traffic management systems.…”

Impulsive control and synchronization of spatiotemporal chaos

“…The equations in (26) and (27) are systems of ODEÕs that can be approximated by the variational systems, given by…”

“…The asymptotic stability of the error dynamics is established, assuring the synchronization between the two systems, and an upper bound on the time intervals between the impulses is obtained. A generalization of this particular type of synchronization to time-varying impulse intervals has been further developed in [27], where less conservative conditions on the Lyapunov function are obtained in the sense that it is required to be non-increasing along a subsequence of the switching. The applications of impulsive synchronization to secure communications have been also developed [40,41].…”