Robust predictor based control of state multiplicative noisy retarded systems

Linear, continuous-time systems with stochastic uncertainties and delayed input are considered. The problems of H_∞ state-feedback control and static output-feedback control are solved, for nominal systems, applying a Luenberger-type predictor. The two problems are solved via the input–output approach, where the system is replaced by a non-retarded system with deterministic norm-bounded uncertainties. The cost function in these two problems is the expected value of the standard H_∞ performance index with respect to the stochastic parameters. The above problems are solved also for the case where the deterministic parameters of the system encounter either norm-bounded or polytopic-type uncertainties. In the uncertain state-feedback control problem the solution is obtained by applying a vertex-dependent approach that is based on the Finsler lemma. An illustrative example is given that compares several control solution methods. An additional example of practical process control problem is also solved.