Design of a high gain regulator by the multiple time scale approach

In this paper a design procedure of the high gain feedback control for a linear time-invariant system is presented. To reveal the structure of the high gain system, a new decoupling concept is introduced. It divides a system into two parts: a zero-free part which is influential in the outputs, and an unobservable part which contains all transmission zeros. In view of the singular perturbation theory with multiple time scales, the high gain feedback control with multiple gain parameters is designed for the zero-free system. The stabilizability of the unobservable part is discussed in relation to a minimal phase property of the plant. The proposed design procedure consists only of elementary operations of matrices, and an illustrative example shows its effectiveness.