Robust Stability and Robust Stabilization of Discrete-Time Markov Jump Linear Systems Under a Class of Stochastic Structured Nonlinear Uncertainties

Robust stability/stabilization for discrete-time time-varying Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations is addressed in this paper. Using a scaling technique, we succeed in effectively addressing the multi-perturbations case. We obtain an estimation of the lower bound of the stability radius in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov difference equations. In the time-invariant case, we show that such a lower bound is actually the exact value of the stability radius. Using the obtained result, we effectively address the state-feedback robust stabilization problem.