Robust control of stochastic systems with noise dependent states and inputs under Markovian switching

A problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching and random diffusion (noise) is considered. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. Sufficient conditions based on linear matrix inequalities (LMI´s) for stochastic stability is obtained. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.