Mathematics – Optimization and Control
Scientific paper
2009-01-15
Applied Mathematics & Optimization, Volume 63, Number 2, pp. 217-237, 2011
Mathematics
Optimization and Control
Revised. 17 pages. To appear in Applied Mathematics & Optimization
Scientific paper
10.1007/s00245-010-9117-6
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for $L_1$-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in $L_1$. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.
Chatterjee Debasish
Pal Soumik
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