Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay

The stochastic stability and robust stochastic stabilisation for time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on stochastic Lyapunov functional, a delay-dependent linear matrix inequalities (LMIs) condition for the time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is given. With this condition, the problem of robust stochastic stabilisation is solved. A numerical example to illustrate the effectiveness of the method is given.