Stability and stabilization of a class of nonlinear discrete-time delayed Markov jump systems

The stability and stabilization problems for a class of nonlinear discrete-time Markov jump systems with mode-dependent delays are investigated. The systems under consideration are more general, since their transition probabilities of the mode jumps can be partly unknown and they cover the systems with completely known and completely unknown transition probabilities as two special cases. Based on the Lyapunov stability theory and the LMI approach, sufficient conditions are derived to guarantee the stochastic stability of the underlying systems, and the design of the stabilizing controller is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.