Parameterization of reduced-order compensator in the frequency domain

Abstract

Abstract After a brief survey of the relations between time and frequency domain representations of the observer-based linear state feedback loop, the parameterization of the reduced-order compensator is discussed. It is shown that the free design parameters are the coefficients in the polynomial matrices and , characterizing the closed-loop dynamics in the frequency domain. Starting from these polynomial matrices, the doubly coprime fractional representations of the system and of the compensator transfer matrices can directly be computed without recurrence to the time domain results. From these representations the right and left coprime compensator matrix fraction descriptions can easily be evaluated using standard algorithms.