Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities

In this work, we investigate the H_∞ control problem for a class of linear discrete-time systems with Markovian jump parameters. The jump parameters considered here are modeled by a discrete-time Markov process. Our attention is focused on the design of a state feedback controller such that both stochastic stability and a prescribed H_∞ performance are required to be achieved when the real system under consideration is affected by both unknown nonlinearity and norm-bounded real time-varying uncertainties. Sufficient conditions are proposed to solve the above problem, which are in terms of a set of solutions of linear matrix inequalities (LMIs)