Delay-dependent Robust Control for Uncertain Linear Systems with Distributed and Multiple Delays

Abstract

This paper considers robust control of uncertain linear neutral systems with multiple state and state derivative delays. With equivalent descriptor representation, the stabilization problem is extended to more general class of neutral-type uncertain linear systems with discrete and distributed delays. The parametric uncertainties are time varying and unknown but norm bounded. Two delay-dependent/independent approaches are proposed to design robust controllers for a class of uncertain linear neutral systems with parametric uncertainty, discrete and distributed multiple delays. Using a presented descriptor model and an appropriate Lyapunov functional, sufficient conditions for closed loop stability are given in terms of linear matrix inequalities (LMIs). Solving the LMI problems, a robust memoryless state feedback is designed for all admissible uncertainties. The results depend on the size and varying rate of the delays. Two examples are provided to show the effectiveness of the proposed strategy.