An entropy-based bound for the computational complexity of a switched system
Name
1907.00655.pdf
Description
Accepted version
Size
649.97 KB
Format
Adobe PDF
Checksum (MD5)
ff379a27b1642034549e48f1915d8485
Author(s)
Legat, Benoit
Parrilo, Pablo A
Jungers, Raphael M
Date Issued
2019
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
© 2019 IEEE. 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 analyze 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.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TAC.2019.2902625
