Stability Analysis of Semi-Markov Jump Stochastic Nonlinear Systems
Xiaotai Wu, Peng Shi, Yang Tang, Shuai Mao, Feng Qian
Abstract
The problem of exponential stability for semi-Markov jump stochastic nonlinear systems is studied in this article. Semi-Markov chain is well known as an extension of the Markov chain, whose sojourn time distribution depends on the current and next states, and is no longer limited to the exponential distribution. However, in the existing works, the independence and the distribution function limitation are imposed on the sojourn time of semi-Markov jump systems. In this article, without additional constraints for the sojourn time, the problem of almost surely exponential stability is investigated for semi-Markov jump stochastic nonlinear systems by developing a new stochastic analysis method. In addition, mode-dependent linear comparable relationships are assumed among Lyapunov like functions, which can effectively reduce the conservatism caused by mode-independent case. To validate the developed theoretic results, two examples are provided in this article.