Controller Synthesis to Render a Closed Loop Transfer Function Positive Real

In this paper we study the problem of synthesizing an internally stabilizing controller for a given plant such that a given closed loop transfer function is extended strictly positive real. Necessary and sufficiency conditions for the existence of controllers are obtained State space formulate 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. These results have immediate applications in robust/nonlinear control.