Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Volume 49, No. 4, Year 2002
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In this brief, we investigate the H∞ control problem for a class of nonlinear discrete-time systems with Markovian jump parameters. The jump parameters considered here is modeled by a discrete-time Markov process. Our attention is focused on the design of 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).