An augmented result on almost sure exponential stability of semi-Markov jump systems

The purpose of this paper is to study almost sure exponential stability for a class of semi-Markov jump systems. A novel type of coupled Lyapunov function is constructed by using the holding time of semi-Markov modes. Then, based on the ergodicity and stationary distribution of semi-Markov switching process, sufficient stability conditions are proposed for semi-Markov jump systems, which significantly improve several known results on almost sure exponential stability. Finally, an example is given to show the superiority of our conclusion. •Study almost sure stability semi-Markov systems with general transition probability.•A new weighted Lyapunov function is proved based on the length of random holding time.•Augmented sufficient conditions are proved by ergodicity to improve known results.•The converge rate of the system is optimized due to the release of some constraints in LMI.