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

Legat, Benoît;Parrilo, Pablo A.;Jungers, Raphaël
(2019) IEEE Transactions on Automatic Control — p. 1 (2019)

Files

190700655.pdf
  • Open Access
  • Adobe PDF
  • 649.97 KB
Download

Details

Authors
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.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Legat, B., Parrilo, P. A., & Jungers, R. (2019). An entropy-based bound for the computational complexity of a switched system. IEEE Transactions on Automatic Control, 1. https://doi.org/10.1109/TAC.2019.2902625 (Original work published 2019)