On the stability of planar randomly switched systems
By M. Benaim, St'ephane Le Borgne, Florent Malrieu, Pierre-André Zitt. 2012
62 citations recorded by the source corpus.
Consider the random process (Xt) t>0 solution of u Xt = AItXt where (It) t>0 is a Markov process on f 0;1g and A0 and A1 are real Hurwitz matrices on R 2 . Assuming that there exists � 2 (0;1) such that (1 − � )A0 + �A 1 has a positive eigenvalue, we establish that k Xtk may converge to 0 or +1 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 [2] by Balde, Boscain and Mason.
Subfields: Control and Systems Engineering, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/35ad920fa5e498e028cdbefc8d1683bc79b7ad10
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In Statistical and Nonlinear Physics
Citations in the corpus
- Qualitative properties of certain piecewise deterministic Markov processes (2012, background): “Nevertheless, as shown in [5], the stability of Markov processes driven by an infinitesimal generator as (2) may depend on the jump rates.”
- Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder” (2014, background): “The transitions from extinction of species y to extinction of species x when the jump rate parameter t increases is reminiscent of the transition occurring with linear systems analyzed in [6] and [26].”