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Zbl 1090.93029
Yang, Haifeng; Xie, Guangming; Chu, Tianguang; Wang, Long
Commuting and stable feedback design for switched linear systems. (English)
[J] Nonlinear Anal., Theory Methods Appl. 64, No. 2, A, 197-216 (2006). ISSN 0362-546X

Summary: Commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.

MSC 2000:: *93C57 Sampled-data control systems
93B52 Feedback control
93D15 Stabilization of systems by feedback

Keywords: Switched linear systems; Commuting and stable feedback design; Common admissible eigen-vector set

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