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2013 On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems
Sendren Sheng-Dong Xu, Chih-Chiang Chen
Abstr. Appl. Anal. 2013(SI56): 1-11 (2013). DOI: 10.1155/2013/681523

Abstract

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among N unstable linear systems and N unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

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Sendren Sheng-Dong Xu. Chih-Chiang Chen. "On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems." Abstr. Appl. Anal. 2013 (SI56) 1 - 11, 2013. https://doi.org/10.1155/2013/681523

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095231
MathSciNet: MR3126750
Digital Object Identifier: 10.1155/2013/681523

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI56 • 2013
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