In this paper, we first review the new algorithm for the two-stage feedback controller design of linear discrete-time systems, and then provide conditions for its applicability. The design algorithm is specialized and simplified for a class of linear systems with slow and fast modes (multitime scale systems or singularly perturbed systems). The proposed design significantly reduces computational full-state feedback design requirements and provides independent and accurate feedback controller design techniques in slow and fast time scales. We present also conditions needed for applicability of the proposed two-stage design in two time scales. The power of the two-stage design lies in the fact that different types of controllers can be designed for different subsystems using the corresponding feedback gains obtained by performing calculations only with the subsystem (reduced-order) matrices.

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