Composite feedback control of discrete multiparameter singularly perturbed systems

The problem of assigning all the poles of a closed-loop system in the specific disc D(alpha, r)by composite state feedback control is considered for discrete multiparameter singularly perturbed systems. A pole assignment of this kind is referred to as a D-pole placement. A D-stability criterion for discrete systems is first proposed; a two-stage method is then developed to analyse the stability relationship between discrete multiparameter singularly perturbed systems and their corresponding slow and fast subsystems. Thereafter, the upper bound of, the ratio of the maximum eigenvalue in the fast subsystem to the minimum eigenvalue in the slow subsystem, is derived such that D-stability of the slow and fast subsystems implies that of the original system, provided that is within this bound. Finally, we propose an algorithm to design a composite feedback control law (i.e. the sum of slow control and fast control) to render the controlled discrete multiparameter singularly perturbed system D(alpha, r)-stable.