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arXiv · 1405.1857

Deterministic and probabilistic algorithms for stabilizing discrete-time switched linear systems

Atreyee Kundu·Niranjan Balachandran·Debasish Chatterjee
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Abstract

In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the switching signal is expressed as an infinite walk on this weighted digraph. We employ graph-theoretic tools and discuss different algorithms for designing walks whose corresponding switching signals satisfy the stabilizing switching conditions proposed in [12]. We also address the issue of how likely/generic it is for a family of systems to admit stabilizing switching signals, and under mild assumptions give sufficient conditions for the same. Our solutions have both deterministic and probabilistic flavours.

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Atreyee Kundu, Niranjan Balachandran, Debasish Chatterjee. 2014-05-08. Deterministic and probabilistic algorithms for stabilizing discrete-time switched linear systems. https://doi.org/10.3934/mcrf.2019009

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