Multiple Lyapunov functions approach to observer-based control for switched systems

Li-li Li, Jun Zhao and Georgi Dimirovski

International Journal of Systems Science, 2013, vol. 44, issue 5, 812-819

Abstract: This article investigates the issue of H∞ control for a class of continuous-time switched Lipschitz nonlinear systems. None of the individual subsystems is assumed to be stabilisable with H∞ disturbance attenuation. Based on a generalised multiple Lyapunov functions (GMLFs) approach, which removes the nonincreasing requirement at switching points, a sufficient condition for the solvability of the H∞ control problem under a state estimation-dependent switching law is presented. Observers, controllers and a switching law are simultaneously designed. As an extension, a sufficient condition for exponential stabilisability is also given.

Date: 2013
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DOI: 10.1080/00207721.2011.625479

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