Composite control of discrete singularly perturbed systems with stochastic jump parameters

In this paper, singular perturbation approach is presented to study discrete systems with stochastic jump parameters. The feedback controller design is decomposed into the design of slow and fast controllers which are combined to form the composite control. The multirate control structure allows the designer to accommodate multiple information rates and to implement the required control computations. Conditions for complete separation of slow and fast regulator designs are given. It is shown that the composite feedback control is O(ε) close to the optimal one, which yields an O(ε²) approximation of optimal performance.