Delay-dependent robust resilient $$H_\infty $$ H ∞ control for uncertain singular time-delay system with Markovian jumping parameters

Abstract

This paper is concerned with the delay-dependent robust resilient $$H_\infty $$ control problem for uncertain singular time-delay system with Markovian jumping parameters. First, a delay-dependent bounded real lemma in terms of linear matrix inequalities is established, which guarantees the nominal Markovian jump singular system to be regular, impulse free and stochastically stable. Then, based on this condition, sufficient conditions in terms of LMIs are given to ensure the existence of the desired robust resilient $$H_\infty $$ controllers. The uncertainties of the controllers are considered in two cases, that is the additive controller gain uncertainties and the multiplicative controller gain uncertainties. Finally, numerical examples illustrate the applicability of the results proposed in this paper.