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

The purpose of this paper is to give a state-space characterization of all internally stabilizing finite-dimensional linear time-invariant controllers for a given finite-dimensional linear time-invariant plant which ensure that the resulting closed-loop transfer function is extended strictly positive real. Both state feedback and output feedback cases are examined. The development uses only elementary ideas beginning with a change of variables and the extended strictly positive real lemma, thus the proofs are simple and clear.