Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H ∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounde...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 146; no. 3; pp. 745 - 763
Main Authors Xu, S. Y., Yang, Y.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.09.2010
Springer
Springer Nature B.V
Subjects
Applications of Mathematics
Applied sciences
Calculus of Variations and Optimal Control; Optimization
Computer science; control theory; systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Controllers
Engineering
Equilibrium
Exact sciences and technology
Feedback control systems
Mathematics
Mathematics and Statistics
Noise
Operations Research/Decision Theory
Optimization
Studies
Theory of Computation
Robust synchronization
LMI
Multiple equilibria
Nonlinear systems
Chaos
dynamic control
Nonlinear system
H infinite control
Non linear control
Feedback regulation
Control synthesis
Synchronization
Non linear system
Phase locked loop
Closed feedback
Linear matrix inequality
Output feedback
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ISSN0022-3239
1573-2878
DOI10.1007/s10957-010-9689-y

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Summary:This study concerns with the robust H ∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H ∞ performance. The derived methods can be applied to the robust H ∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9689-y