Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

Abstract

The purpose of this note is to study impulsive control and synchronization of memristor based chaotic circuits shown by Muthuswamy. We first establish a less conservative sufficient condition for the stability of memristor based chaotic circuits. After that, we discuss the effect of errors on stability. Meanwhile, we also discuss impulsive synchronization of two memristor based chaotic systems. Our results are more general and more applicable than the ones shown by Yang, Li, and Huang. Finally, several numerical examples are given to show the effectiveness of our methods.

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

“…Figure 13: Relation between the number of quantization levels and its complexity: (a) quantization method one; (b) quantization method two. 13 Complexity…”

“…As a matter of fact, memory electronic elements are usually designed nonlinearly. Thus, chaos can be easily found in those memory electronic element-based circuits [8][9][10][11][12][13][14][15][16]. Bao et al [8][9][10][11] presented many valuable works on chaotic memristor circuits.…”

Exponential stability analysis of nonlinear systems with bounded gain error

“…Impulsive control of nonlinear systems has been one of the focal points in many research and application fields, such as complex networks, orbital transfer of satellite, dosage supply in pharmacokinetics, ecosystems management, synchronization in chaotic secure communication systems [9][10][11][12][13][14][15], etc. Impulsive control can stabilize nonlinear systems by using it only at some isolated points.…”

The Exponential Stabilization of a Class of n-D Chaotic Systems via the Exact Solution Method

“…Now, it is generally agreed that this complex and irregular phenomenon is useful because it has many applications in some areas such as secure communications and information sciences [1]. For the purpose of utilizing chaotic signals, the chaos control and chaos synchronization of dynamical systems have attracted a wide range of research activities for over two decades [2][3][4][5][6][7][8]. A wide variety of approaches have been proposed for achieving chaos control and synchronization which include adaptive control method [9], sliding mode control [10,11], predictive control method [12], and backstepping method [13].…”