An entropy-based bound for the computational complexity of a switched system
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.
Cite
@article{arxiv.1907.00655,
title = {An entropy-based bound for the computational complexity of a switched system},
author = {Benoît Legat and Pablo A. Parrilo and Raphaël M. Jungers},
journal= {arXiv preprint arXiv:1907.00655},
year = {2019}
}
Comments
8 pages, 4 figures, will appear in IEEE Transactions on Automatic Control. arXiv admin note: substantial text overlap with arXiv:1710.01814