Finite-time stabilisation for Markov jump systems with Gaussian transition probabilities

Abstract

The problems of finite-time analysis and design for a class of Markov jump systems with Gaussian transition probabilities (TPs) are investigated in this study. Gaussian TP density function is introduced to quantise the stochastic uncertain information of TPs. Mode-dependent and variation-dependent controller is designed to make the resulting closed-loop systems finite-time bounded and finite-time stabilisable for all admissible unknown external disturbances and random uncertain TPs. It is shown that the approach proposed in the paper dealing with TPs outperforms available ones in literature to date, which is also confirmed by a numerical example.