A Converse Lyapunov Theorem and Robustness for Asymptotic Stability in Probability

作者：Teel Andrew R^*; Hespanha Joao P; Subbaraman Anantharaman

来源：IEEE Transactions on Automatic Control, 2014, 59(9): 2426-2441.

DOI：10.1109/TAC.2014.2322431

• Global asymptotic stability
• Lyapunov function

A converse Lyapunov theorem is established for discrete-time stochastic systems with non-unique solutions. In particular, it is shown that global asymptotic stability in probability implies the existence of a continuous Lyapunov function, smooth outside of the attractor, that decreases in expected value along solutions. The keys to this result are mild regularity conditions imposed on the set-valued mapping that characterizes the update of the system state, and the ensuing robustness of global asymptotic stability in probability to sufficiently small state-dependent perturbations.

• 出版日期2014-9