Dissipativity-based $\mathcal{L}_2$ gain-scheduled static output feedback design for rational LPV systems

TL;DR

This paper introduces a dissipativity-based method for designing gain-scheduled static output feedback controllers for rational LPV systems, ensuring stabilization and $\\mathcal{L}_2$ performance with a simple, non-interactive approach.

Contribution

It develops a novel dissipativity-based framework using QSR dissipativity, Finsler's Lemma, and linear annihilators to formulate LMIs for controller design in rational LPV systems.

Findings

Effective stabilization demonstrated through numerical examples.

No restrictions on plant output matrix.

Simple, non-interactive design procedure.

Abstract

This paper proposes the design of gain-scheduled static output feedback controllers for the stabilization of continuous-time linear parameter-varying systems with $\mathcal{L}_2$-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.