In this work we deal with the asymptotic stabilization problem of polynomial (and rational) input-affine systems subject to parametric uncertainties. The problem of linear static output feedback (SOF) control synthesis is handled, having as a prerequisite a differential algebraic representation (DAR) of the plant. Using the property of strict QSR-dissipativity, theFinsler's Lemma and the notion of linear annihilators we introduce a new dissipativity-based strategy for robust stabilization which determines a static feedback gain by solving a simple linear semidenite program on a polytope. At the same time, an estimate of the closed-loop domain of attraction is given in terms of an ellipsoidal set. The novelty of the proposed approach consists in this combination of dissipativity theory and powerful semidenite programming(SDP) tools allowing for a simple solution of the challenging problem of static output feedback design for nonlinear systems. A numerical example allows the reader to verify the applicability of the proposed technique.

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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.

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