Stabilization of switched linear systems by using projections

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• 作者：C. Pé ; rez ; ^{carmen.perez@uca.es} ; F. Bení ; tez ; J.B. Garcí ; a-Gutié ; rrez
• 关键词：Projections ; Stabilization ; Switched systems ; Conic switching law ; Output feedback stabilization
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：July 2017
• 年：2017
• 卷：318
• 期：Complete
• 页码：117-123
• 全文大小：404 K
• 卷排序：318

文摘

This paper proposes a new approach to stabilize switched linear systems. In this method, the projections are employed to establish the stabilization of a switched systems class. Hence, we suppose that the subsystems given by a switched linear system can be projected to the same subspace. Under these conditions, we prove that this switched linear system is stabilizable if and only if a low-order switched linear system is also stabilizable. In order to complete this study, we present a counter example that proves that it is not always possible to use the projections. Moreover, the main result in the paper is applied to solve the stabilization of a third-order switched systems class and the static feedback stabilization of a switched linear systems class. Finally, a numerical example is included in order to illustrate the new method obtained to stabilize a third-order switched systems class.