Certifying Unstability of Switched Systems Using Sum of Squares Programming
Name
18m1173460.pdf
Description
Published version
Size
625.41 KB
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Unknown
Checksum (MD5)
e37a67679d1eb25bfcae0403a5224406
Author(s)
Legat, Benoît
Parrilo, Pablo A.
Jungers, Raphaël
Date Issued
2020
Journal
SIAM Journal on Control and Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Society for Industrial and Applied Mathematics 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 investigate dual formulations for this approach and leverage these dual programs for developing new analysis tools for the JSR. We show that the dual of this convex problem searches for the occupations measures of trajectories with high asymptotic growth rate. We both show how to generate a sequence of guaranteed high asymptotic growth rate and how to detect cases where we can provide lower bounds on the JSR. All results of this paper are presented for the general case of constrained switched systems, that is, systems for which the switching signal is constrained by an automaton.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/18M1173460
