Delay-dependent robust stability and H∞ control of jump linear systems with time-delay

This paper considers the class of continuous-time jump linear systems with time-delay and polytopic uncertain parameters. When the time-delay is a known constant, by using the linear matrix inequality (LMI) technique, we first establish delay dependent sufficient conditions for robust stability and robust H-infinity control of the class of systems under study. The problem of determining the maximum time-delay under which the system will remain stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. When the control input contains a time-delay, an algorithm to design a state feedback controller with constant gain matrix is developed. Two examples are given to show the validness of the theoretical results.