Robust Stabilization for Uncertain Saturated Time-Delay Systems: A Distributed-Delay-Dependent Polytopic Approach

This technical note investigates the robust stabilization problem for uncertain linear systems with discrete and distributed delays under saturated state feedback. Different from the existing approaches, a distributed-delay-dependent polytopic approach is proposed in this technical note, and the saturation nonlinearity is represented as the convex combination of state feedback and auxiliary distributed-delay feedback. Then, by incorporating an appropriate augmented Lyapunov-Krasovskii (L-K) functional and some integral inequalities, the less conservative stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities (LMIs). The effectiveness and reduced conservatism of the proposed conditions are illustrated by numerical examples.