Robust stabilization for uncertain switched neutral systems with interval time-varying mixed delays

Abstract

This paper deals with the problems of exponential stability and stabilization of uncertain switched neutral systems (USNSs) with interval time-varying mixed delays. Interval time-varying delay exists in the state, derivatives of the state (neutral), and the output. This research emphasizes the cases where uncertainties are norm-bounded time-varying in the model. First, sufficient conditions are proposed in terms of a set of linear matrix inequalities (LMIs) to guarantee exponential stability using the average dwell time (ADT) approach and the piecewise Lyapunov function technique. Then, the corresponding conditions are obtained for the stabilization via a dynamic output feedback (DOF) controller. The problem of uncertainty in the system model is solved by designing the DOF controller and applying the Yakubovich lemma. Since the conditions obtained are not represented by LMI form, decoupling between the Lyapunov function and the system matrices is generated using the proposed slack matrix variable, and a new condition is obtained. Finally, numerical examples are given to determine the effectiveness of the proposed theorem.