Asynchronous H∞ control of semi-Markov jump linear systems

摘要

This paper addresses the asynchronous H∞ control problem for a class of continuous-time semi-Markov jump linear systems. Under the assumption that the system mode is not accessible, we introduce a discrete-state and continuous-time process which is related to the system mode by a conditional probability as a switching signal of the controller. By constructing a semi-Markov-based Lyapunov funcational, a sufficient condition to ensure the stability of the system with a prescribed H∞ performance is established. In addition, an equivalent statement is derived by introducing a slack variable, and the asynchronous controller is designed. Two examples are presented to illustrate the effectiveness of the proposed new design method.