High-order moment stabilization for Markov jump systems with attenuation rate

This paper studies the high-order moment control problem for discrete-time Markov jump linear systems (MJLSs) with certain dynamic response performance and disturbance rejection specifications. An appropriate cumulant generating function is employed to express the original stochastic system in high-order component form. This facilities the high-order moment stabilization of MJLSs. Moreover, a pole region assignment approach is utilized to ensure desired dynamic response specifications with a certain attenuation rate. An arithmetic and geometric inequality approach is utilized to extract sufficient conditions ensuring the designed controller existence. These conditions ensure the high-order moment steady-state property and certain dynamic specifications for the MJLSs. The effectiveness of the proposed method is demonstrated through numerical and practical examples.