On the stability of planar randomly switched systems
Probability
2012-04-10 v1 Dynamical Systems
Optimization and Control
Abstract
Consider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2. Assuming that there exists lambda in (0, 1) such that (1 - \lambda)A0 + \lambdaA1 has a positive eigenvalue, we establish that the norm of Xt may converge to 0 or infinity, depending on the the jump rate of the process I. An application to product of random matrices is studied. This paper can be viewed as a probabilistic counterpart of the paper "A note on stability conditions for planar switched systems" by Balde, Boscain and Mason.
Keywords
Cite
@article{arxiv.1204.1921,
title = {On the stability of planar randomly switched systems},
author = {Michel Benaïm and Stéphane Le Borgne and Florent Malrieu and Pierre-André Zitt},
journal= {arXiv preprint arXiv:1204.1921},
year = {2012}
}