In this paper the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear time-varying systems and Linear Differential Inclusions. We also present preliminary results on another related problem; namely, the construction of multiple polyhedral Lyapunov functions for specifying the existence of stabilising switching sequences. © Springer-Verlag 2004.
CITATION STYLE
Yfoulis, C. A., & Shorten, R. (2004). A numerical technique for stability analysis of linear switched systems. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2993, 631–645. https://doi.org/10.1007/978-3-540-24743-2_42
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