State feedback stabilization of time-varying delay uncertain systems: A delay decomposition approach

Abstract

This paper focuses on the problem of asymptotic stabilization for time-varying delay uncertain systems. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stabilization criteria are obtained in terms of linear matrix inequalities (LMIs). Based on this, a delay-dependent sufficient condition for the existence of a state feedback controller ensuring stability of the closed-loop dynamics is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between terms in the Leibniz–Newton formula into account. Integral inequality approach (IIA) and delay decomposition approach are used to express this relationship and linear matrix inequalities (LMIs)-based algorithm to design the controller stabilizing the system.