Robust Cascaded sub-Predictors Control of Norm-bounded Stochastic Systems

We consider linear input-delayed stochastic uncertain state-multiplicative systems in the discrete-time setting. The system uncertainties include both norm-bounded and polytopic type ones. An H ∞ single predictor control is applied to the norm-bounded uncertain system assuming the system states are accessible, thus rendering the system to a state delayed one and resulting in a single LMI condition. The latter application is extended to the case where an assembly of two sub-predictors are applied, resulting in an improved performance of the closed-loop control system. The solution obtained for the norm-bounded uncertain case is extended to the case where the system matrices reside in given polytope. An example is given that demonstrates the applicability of the theory.