Energy and power optimization in a behavioural framework

We deal with a number of quadratic optimization problems in the behavioural framework, in the spirit of the classical linear quadratic regulator problem for systems in state-space form. The central theme is dissipativity of the system at hand: we interpret our problems in terms of the exchange of energy between the system and the outside world. Using the Kalman-Yakubovich-Popov lemma in the behavioural framework, we arrive at energy and power optimizing control laws in terms of the solutions to a linear matrix inequality in the original data that is used to specify the problems.