Delay-dependent H∞ control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control

This paper deals with the problem of robust normalization and delay-dependent H∞ control for a class of singular Markovian jump systems with norm-bounded parameter uncertainties and time delay. A new impulsive and proportional-derivative control strategy with memory is presented, which results in a novel class of hybrid impulsive systems. Sufficient conditions are developed to guarantee that the resultant closed-loop system is not only robust normal and stochastically stable, but also satisfies a prescribed H∞ performance level for all delays no larger than a given upper bound. In addition, the explicit expression of the desired impulsive control gains is also given together with the design approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.