Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

Liping Chen; Yi Chai; Ranchao Wu

doi:10.1063/1.3650237

Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

Chaos. 2011 Dec;21(4):043107. doi: 10.1063/1.3650237.

Authors

Liping Chen¹, Yi Chai, Ranchao Wu

Affiliation

¹ State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044, China. lip_chen@yahoo.com.cn

PMID: 22225344
DOI: 10.1063/1.3650237

Abstract

This paper is devoted to synchronization of uncertain fractional-order chaotic systems with fractional-order α: 0 < α < 1 and 1 ≤ α < 2, respectively. On the basis of the stability theory of fractional-order differential system and the observer-based robust control, two sufficient and necessary conditions for synchronizing uncertain fractional-order chaotic systems with parameter perturbations are presented in terms of linear matrix inequality, which is an efficient method and could be easily solved by the toolbox of MATLAB. Finally, fractional-order uncertain chaotic Lü system with fractional-order α = 0.95 and fractional-order uncertain chaotic Lorenz system with fractional-order α = 1.05 are taken as numerical examples to show the validity and feasibility of the proposed method.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Computer Simulation
Feedback
Linear Models*
Models, Statistical*
Nonlinear Dynamics*