Dissipativity-based ℒ2 gain-scheduled static output feedback design for rational LPV systems

This paper proposes the design of gain-scheduled 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 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, in many cases, 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.