LMI-based robust H∞ control of uncertain linear jump systems with time-delays

Abstract

This paper examines the robust mean square stabilization and robust H ∞ control problem for a class of linear systems. The systems under consideration involve time delays, parameter uncertainties, and jumping parameters which may be seen as, for example, failures that occur in the systems at certain probabilities. The uncertain parameters are assumed to be time-varying and satisfy boundness conditions. A systematic approach via linear matrix inequalities (LMI) is proposed to solve the problem of concern. Sufficient conditions for robust mean square stabilization and robust H ∞ control are given in the form of LMI and the control law is computed using standard LMI techniques.