Stabilization of planar discrete-time switched systems: Switched Lyapunov functional approach |
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Authors: | Yuan Gong Sun Long Wang |
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Affiliation: | aSchool of Mathematical Science, Qufu Normal University, Qufu 273165, China;bCenter for Systems and Control, College of Engineering, Peking University, Beijing 100871, China |
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Abstract: | In this paper, we investigate the problem of stabilization for single-input planar discrete-time switched systems by establishing necessary and/or sufficient conditions for the existence of switched quadratic Lyapunov functions of the closed-loop system. The results given in terms of a series of matrix inequalities generalize those results in our recent paper [Y.G. Sun, L. Wang, G. Xie, Necessary and sufficient conditions for stabilization of discrete-time planar switched systems, Nonlinear Anal.: Theory and Methods 65 (2006) 1039–1049] and clearly describe the set of switched quadratic Lyapunov functions for the system. |
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Keywords: | Discrete-time switched system Stabilization Switched quadratic Lyapunov function Necessary and sufficient condition |
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