Dissipative control systems synthesis with full state feedback

In this paper we present a general framework for synthesizing state feedback controllers to achieve any desired closed loop dissipative behavior. Special cases include positive real and H(infinity) controller synthesis. We show that the solution to this dissipative controller synthesis problem is equivalent to the existence of a solution to a partial differential inequality (nonlinear systems case) or an algebraic Riccati inequality (linear systems case). Stability results can be obtained under appropriate detectability assumptions, and a generalization of the strict bounded real lemma is given. We also present an application of the results to a robust stabilization problem.