Solution to the positive real control problem for linear time-invariant systems

We study the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear time-invariant plant such that a given closed-loop transfer function is extended strictly positive real. Necessary and sufficient conditions for the existence of a controller are obtained. State-space formulas for the controller design are given in terms of solutions to algebraic Riccati equations (or inequalities). The order of the constructed controller does not exceed that of the plant.>