pth moment stability of discrete-time Markov jump systems by extended system method

This paper studies the pth moment stability of discrete-time Markov jump systems by utilizing the extended system method, which is composed of the operator spectrum technique and the ℋ-representation technique. Firstly, some extended systems are constructed by the operator spectrum technique and the ℋ-representation technique to transform the discrete-time Markov jump systems into the extended systems. Furthermore, the relationship in pth moment stability between the extended systems and the stochastic systems is discussed. Next, with the help of the extended systems, the necessary and sufficient conditions for the even-order moment stability, and several sufficient conditions/necessary conditions for the odd-order moment stability are obtained, respectively. Additionally, as applications of the extended system method, observability and detectability in pth moment sense are discussed, and the necessary and sufficient conditions for observability and detectability in even-order moment are obtained, respectively. Finally, several examples are given to illustrate the validity of the results.