Feedback control of nonlinear systems using passivity indices

This paper presents a new controller design framework for nonlinear feedback systems using passivity indices. These indices measure the level of passivity of a system and can be used to set lower bounds to the parameters of a stabilizing controller. We provide a systematic way of designing a dynamic output feedback controller based on a matrix condition on the plant dynamics and its passivity indices. Instead of demanding the solution of partial differential equations and the derivation of Casimir functions, as it is the case of most control by interconnection methods, our strategy relies solely on algebraic conditions. This issue simplifies the controller design considerably. We assume that all functions involved are polynomials. Lyapunov stability of the closed-loop is addressed. An example is provided in order to demonstrate the applicability of the proposed method.