Master-slave synchronization of chaotic systems with a modified impulsive controller

Abstract

This paper investigates global exponential synchronization of chaotic systems by designing a novel impulsive controller. The novel impulsive controller is a combination of current and past error states, which is a modification of the normal impulsive one. Some global exponential stability criteria are derived for the error system by utilizing the stability analysis of impulsive differential equations and differential inequalities and, moreover, the exponential convergence rate can be specified. An illustrative example is given to show the effectiveness of the modified impulsive control scheme.

Chua's Circuit: Control and Synchronization

“…7. We used a Master-Slave configuration with direct communication between them [Yalcin et al, 2001;Mkaouar & Boubaker, 2012;Feng & Cao, 2013]. The communication from the "Master" circuit to the "Slave" one was done through a repeater, so that the information is transmitted to be one-directional.…”

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

“…6,10- 14 Takagi-Sugeno (T-S) fuzzy logic system is a wonderfully handy tool that has been proposed by Takagi and Sugeno, 15 which presents nonlinear systems through a group of "IF-THEN" rules via "blending" all subsystems with membership functions, and it can uniformly approximate any continuous function on a compact set with random accuracy. 6,10- 14 Takagi-Sugeno (T-S) fuzzy logic system is a wonderfully handy tool that has been proposed by Takagi and Sugeno, 15 which presents nonlinear systems through a group of "IF-THEN" rules via "blending" all subsystems with membership functions, and it can uniformly approximate any continuous function on a compact set with random accuracy.…”

“…Conventional nonlinear system control approaches suffer from discontented performance resulted from existed input nonlinearities, parametric uncertainties, external disturbances, and time-varying delays. 6,[10][11][12][13][14] Takagi-Sugeno (T-S) fuzzy logic system is a wonderfully handy tool that has been proposed by Takagi and Sugeno, 15 which presents nonlinear systems through a group of "IF-THEN" rules via "blending" all subsystems with membership functions, and it can uniformly approximate any continuous function on a compact set with random accuracy. 16 It should lay great emphasis on T-S fuzzy system, which has better learning capability in modeling nonlinear system with uncertainties than other types of fuzzy systems.…”

New Linear Generalized Synchronization and Parameter Identification between Different Chaotic Systems

“…Since the seminal work in [8], chaos synchronization has been a topic of great attention [9,10], and been applied like dominoes effect in numerous fields including secure communication [11,12], neurocomputing [13], complex systems [14], human brain and coronary artery [15,16,17] and so on. Due to above-mentioned and many potential applications, various different types of chaos synchronization have been developed such as complete synchronization [8,18,19], anti-synchronization [20,21], phase synchronization [22,23,24], lag synchronization [25,26,27], generalized synchronization (GS) [28,29,30,31,32,33,34,35,36,37,38,39,40], exponential synchronization [41], impulsive synchronization [42,43,44,45], etc.…”