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.
This paper deals with robust static output feedback (SOF) stabilization of linear time-invariant (LTI) systems with transient performance. The proposed approach considers uncertainties on the system matrices and does not impose any constraints on the output matrix. We use the definition of strict QSR-dissipativity to formulate new sufficient conditions in the form of linear matrix inequalities (LMIs) for asymptotic stabilization. One of the main advantages of the developed strategy is that in many cases static output feedback can be designed in a non-iterative manner. Numerical examples highlight the effectiveness of the proposed approach.
In this letter, the notion of robust strict QSRdissipativity is applied to solve the static output feedback control problem for a class of continuous-time nonlinear rational systems subject to input saturation and bounded parametric uncertainties. A local dissipativity condition is combined with generalized sector conditions to formulate the stabilization problem in terms of linear matrix inequalities. The strategy applies to general static output feedback design without any restrictions on the plant output matrix. An optimization problem is formulated in order to compute the feedback gain matrix that maximizes the estimate on the closed-loop region of attraction. Numerical examples are provided to illustrate the applicability of this new approach in examples adapted from the literature.
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