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 andH _∞ 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. This work was supported by the Cooperative Research Centre for Robert and Adaptive Systems (CRASys), Australia.