Chua system chaos synchronization using single variable feedback based on LaSalle invariance principal

Abstract

This paper treats the chaos synchronization problem of chaotic Chua circuit system. Based on LaSalle invariance principal, the proposed controller is featured that (a) only single variable information of the master system is needed; (b) the control law is a simple linear controller with low gain. Finally, the effectiveness of the proposed control law is also illustrated by the numerical simulation on Matlab environment.

Synchronization of nonlinearly coupled networks of Chua oscillators

“…The problem of the synchronization of two identical Chua oscillators via the first state variable by linear coupling addressed in Corollary 4 has been also successfully tackled in Chen et al (2010Chen et al ( , 2012 for the case of γ = 0 by employing the Lyapunov method. The constraint on the coupling constant obtained in Chen et al (2010Chen et al ( , 2012 reads as k > α|a|, which is less a conservative condition compared to (21). However, the applicability of Theorem 3 is more general even in the case of two oscillators due to the possibility of γ = 0.…”

“…Synchronization of two linearly coupled Chua oscillators has been studied in Wu and Chua (1994); Wang and Liu (2006); Bowong and Tewa (2009); Wang et al (1999); Zheng et al (2002); Chen et al (2010Chen et al ( , 2012. In Wu and Chua (1994) it is conjectured that synchronization between two chaotic Chua circuits can be achieved by using the second state as the feedback variable for sufficiently large coupling constant.…”

“…This conjecture has been analytically proven in Zheng et al (2002) and Wang et al (1999) utilizing Lyapunov-type arguments and a novel observer design methodology. Using the LaSalle invariance principle, a linear low-gain controller that exploits a single variable feedback (first state coordinate x 1 ) has been constructed in Chen et al (2010). The robustness of this controller with respect to the perturbations of the parameters of Chua oscillators has been studied in Chen et al (2012).…”

Uncertain Lorenz system chaos synchronization using single variable feedback

“…Junan Lu [13] also given out a linear and adaptive controller for an unified chaotic system( unification of Lorenz, Chen and Lu chaotic system) with single variable feedback. Recently, Fengxiang Chen [14] proposes a simple linear controller for Lu system via theory of cascade-connection system, and it can be extended to Lorenz system easily. However, literatures [11]- [14] did not take the parameters uncertainty into account, and thus the synchronization will fail when some uncertainty occurs.…”

“…Recently, Fengxiang Chen [14] proposes a simple linear controller for Lu system via theory of cascade-connection system, and it can be extended to Lorenz system easily. However, literatures [11]- [14] did not take the parameters uncertainty into account, and thus the synchronization will fail when some uncertainty occurs. In this paper, we will provide a nonlinear controller with single variable information of the master system for uncertain Lorenz chaotic system based on stability theory of Lyapunov.…”