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 real lemma, and Youla parameterization, thus the proofs given are simple and clear.