An algorithm to compute invariant sets for third-order switched systems

We study invariant sets for switched systems. We focus on a class of third-order switched systems. In this class of switched systems we solve the problem of finding an invariant set for a switching law. For each switched system we provide the invariant set and the switching law, in addition, the inv...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2017-07, Vol.318, p.348-353
Main Authors: García-Gutiérrez, J.B., Benítez-Trujillo, F., Pérez, C.
Format: Article
Language:English
Subjects:
Invariant set
Switched linear systems
Third-order system
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Summary:We study invariant sets for switched systems. We focus on a class of third-order switched systems. In this class of switched systems we solve the problem of finding an invariant set for a switching law. For each switched system we provide the invariant set and the switching law, in addition, the invariant set is a polyhedral cone and the switching law is switching on the boundary. To accomplish this we reduce the problem to a simplified system. We provide a procedure calculating the invariant set. The method is based on calculating an invariant set for a simplified system and then transformating the invariant set to the original system. We illustrate this method with an example.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.08.048