Delay-Dependent H∞ Control for Singular Time-Varying Delay Systems with Markovian Jumping Parameters

This paper is concerned with the delay-dependent H-infinity control problem for uncertain singular time-varying delay systems with Markovian jumping parameters. First of all, a new Lyapunov-Krasovskii functional is established to develop the new bounded real lemma (BRL). Sufficient condition is given in terms of linear matrix inequalities (LMIs), which guarantees the system to be stochastically admissible with given H-infinity performance index gamma. We employ delay decomposition approach and improved Wirtinger inequality to reduce the conservatism. Secondly, based on this BRL, the explicit expression of the desired feedback controller gain is obtained by solving a set of strict LMIs. And the robust H-infinity controller for uncertain systems is also presented. Finally, some numerical examples are provided to illustrate the effectiveness and less conservativeness of the proposed methods.

Automated summary

This paper focuses on the delay-dependent H-infinity control problem for uncertain singular time-varying delay systems with Markovian jumping parameters. A new Lyapunov-Krasovskii functional and bounded real lemma (BRL) are proposed, and delay decomposition approach and improved Wirtinger inequality are employed to reduce conservatism.