Observer-Based Stabilization of Nonhomogeneous Semi-Markov Jump Linear Systems With Mode-Switching Delays

Abstract

This technical note addresses the problem of simultaneous design of observer and controller for discrete-time nonhomogeneous semi-Markov jump linear systems (S-MJLSs) against mode mismatches between system and observer-based controller. The considered systems are more general than homogeneous S-MJLSs, and the mode mismatches are caused by time delays of mode switchings of controller. Based on the semi-Markov kernel approach, together with the Lyapunov function depending upon not only both the system and controller modes but also the time that has elapsed in the current mode, sufficient conditions on the existence of the desired mode-dependent observer-based controller are presented such that the augmented nonhomogeneous S-MJLS composed of a closed-loop control system and an estimation error system is $\sigma$ -error mean square stable. Finally, a practical example of a quarter-car active suspension is provided to validate the superiorities of the proposed control strategy.