New delay-dependent bounded real lemmas of polytopic uncertain singular Markov jump systems with time delays

This paper addresses the H ∞ performance analysis problem for singular Markov jump delayed systems with polyhedral parameter uncertainties. By introducing two useful inequalities (see Lemma 2), some new bounded real lemmas (BRLs) are obtained based on a novel parameter-dependent Lyapunov functional. The presented BRLs can guarantee that the considered system is stochastically admissible and satisfies a prescribed H ∞ performance level. Two numerical examples are provided to demonstrate the improvement of the proposed method over the existing methods.