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.
This paper proposes the design of gainscheduled static output feedback controllers for the stabilization of continuous-time linear parameter-varying systems with L 2 -gain performance. The system is transformed into the form of a differential-algebraic representation which allows dealing with the broad class of systems whose matrices can present rational or polynomial dependence on the parameter. The proposed approach uses the definition of strict QSR-dissipativity, Finsler's Lemma, and the notion of linear annihilators to formulate conditions expressed in the form of polytopic linear matrix inequalities for determining the gain-scheduled static output feedback control for system stabilization. One of the main advantages of the strategy is that it provides a simple design solution in a non-interactive manner. Furthermore, no restriction on the plant output matrix is imposed. Numerical examples highlight the effectiveness of the proposed method.
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