Abstract:

The stability and stabilization problem for a class of continuous-time Markov jump singular systems is investigated. A sufficient condition is proposed for the Markov jump singular system to be regular, impulse-free and stochastically stable, and the design of the stabilizing controller is presented. Comparing with the previous literature, the system under consideration is more general since their transition probabilities of mode jumps can be partly unknown, and the results are presented in terms of a strict linear matrix inequality. A numerical example shows the effectiveness of the obtained result.