H∞ Asynchronous Control for Discrete-Time Semi-Markov Jump Systems

This paper investigates the problem of H∞ asynchronous control for discrete-time semi-Markov jump systems. In practice, it is difficult to ensure that controller modes and system modes are updated synchronously. Therefore, a hidden semi-Markov model is introduced to characterize such an asynchronous phenomenon between system modes and controller modes. Meanwhile, the switching signal of the controller is generated by a given conditional probability related to the system mode. Based on the mode-dependent and elapsed-time-dependent Lyapunov function, together with the semi-Markov kernel (SMK) method, sufficient conditions constructed by linear matrix inequalities (LMIs) are derived to ensure the existence of an asynchronous controller such that the resulting system is σ-error mean square stable and satisfies an H∞ performance index. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the method proposed.