This thesis contains contributions to some relevant problems in the field of control theory and controller design technology, namely to the areas of passivity analysis and dissipative control synthesis for linear and nonlinear dynamical systems. The first of our contributions consists in presenting a solution to a problem which had been unsolved for many years: the problem of the equivalence between the notions of strict positive realness and strict passivity of linear systems. Both properties imply the asymptotic stability of a linear system, although the former is a frequency-domain concept and the latter is a time-domain concept.

Subsequently, we approach the equally classical topic of static output feedback stabilization of linear systems, a problem to which a definite solution remains to be given. We present a new necessary and sufficient LMI condition for stabilization based on the notion of strict dissipativity, and we propose a new noniterative strategy for controller design which consists in solving a single convex optimization problem.

In addition, we also introduce a new dissipativity-based strategy for feedback stabilization of nonlinear systems using the notion of linear annihilators and the celebrated Finsler’s Lemma. This approach allows for analysing the dissipativity properties of rational nonlinear plants in terms of a polytopic LMI condition. A new stabilizability condition that would not be feasible in the case of a passive representation of the system is presented as well, making it possible to derive a closed-form expresion for the controller’s feedthrough term as a direct consequence of the local dissipativity analysis of the plant. This feature simplifies the remaing steps of the controller design procedure considerably, both in the case of a static or a dynamic output feedback.