State-space characterization of all solutions to positive real control problem

Abstract

The purpose of this paper is to give a state-space characterization of all internally stabilizing finite-dimensional linear time-invariant output feedback controllers for a given finite-dimensional linear time-invariant plant which ensure that the resulting closed-loop transfer function is extended strictly positive real(ESPR). All such controllers are parameterized by a fixed linear fractional transformation with an ESPR, stable free parameter. The parameterized controllers have a state dimension not less than that of the open-loop plant. The development uses only elementarily algebraic ideas beginning with a change of variables, an extended version of Kalman-Yacubovich-Popov positive rear lemma, and Youla parameterization, thus the proofs given are simple and clear.