Section: New Results
On the stability of planar randomly switched systems
Participant : Florent Malrieu.
This is a collaboration with Michel Benaïm (université de Neuchâtel), Stéphane Le Borgne (IRMAR) and Pierre–André Zitt (université de Paris–Est Marne–la–Vallée).
The paper  illustrates some surprising instability properties that may occur when stable ODE's are switched using Markov dependent coefficients. Consider the random process solution of where is a Markov process on and and are real Hurwitz matrices on . Assuming that there exists such that has a positive eigenvalue, we establish that the norm of may converge to 0 or infinity, depending on the the jump rate of the process . An application to product of random matrices is studied. This work can be viewed as a probabilistic counterpart of the paper  by Baldé, Boscain and Mason.