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An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems


D. Chatterjee, S. Pal
Conference/Journal:, Applied Mathematics & Optimization, vol. 63, pp. 217-237, Applied Mathematics & Optimization, Also available at:

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.


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   author = {Debasish Chatterjee and Soumik Pal},
   title = {An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems},
   journal = {Applied Mathematics & Optimization},
   publisher = {Springer New York},
   issn = {0095-4616},
   keyword = {Mathematics and Statistics},
   pages = {1-21},
   url = {},
   note = {10.1007/s00245-010-9117-6},
   year = {2010}
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