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arXiv · 1907.00655

An entropy-based bound for the computational complexity of a switched system

Benoît Legat·Pablo A. Parrilo·Raphaël M. Jungers
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Abstract

The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyse the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the p-radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low rank matrices to the computation of the constrained JSR of matrices of small dimension.

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Benoît Legat, Pablo A. Parrilo, Raphaël M. Jungers. 2019-07-01. An entropy-based bound for the computational complexity of a switched system. https://doi.org/10.1109/tac.2019.2902625

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