Delay-Dependent Stability and Stabilization for Uncertain Discrete Markovian Jump Singular Systems with Mode-Dependent Time-Delay

The robust stochastic stability and stabilization problems for mode-dependent time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a standard linear system, and delay-dependent linear matrix inequality (LMI) condition for the mode-dependent time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is obtained. With this condition, robust stability and stabilization problems are solved, and the LMI sufficient conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.