Stabilisation of semi-Markovian jump stochastic systems via asynchronous switching control

Abstract

Stabilisation of asynchronous switching semi-Markovian jump stochastic systems is discussed in this paper. By the ergodic property of the semi-Markov process and the method of multiple Lyapunov functions, some sufficient conditions for almost sure exponential stability of stochastic systems are formulated, which cover some existing results in the literature. Applications of the obtained results to two special types of systems are then reformulated in a more convenient way. In particular, the non-equally dividing technique is used to construct solvable conditions for asynchronous semi-Markovian jump linear stochastic systems. Numerical examples are performed to verify the obtained theoretical results.