Regional Static Output Feedback Stabilization Based on Polynomial Lyapunov Functions for a Class of Nonlinear Systems

Resumo

Resumo

This paper presents a new method for regional stabilization of discrete-time nonlinear systems by static output feedback based on polynomial Lyapunov functions. The considered class of nonlinear systems subject to time-varying parameters can be described by difference-algebraic representation and an equivalent polytopic model is obtained, making it possible to apply Lyapunov theory and linear matrix inequality-based tool. In this sense, a convex optimization problem in terms of LMI is provided to guarantee the closed-loop system’s robust stabilization and to enlarge the estimated domain of attraction (DoA). The proposed control design is a one-step approach that can be applied to systems with nonlinear output matrices. It requires no iterative algorithms or congruence transformation, and auxiliary decision variables are introduced only aiming at less conservative results. Besides that, the use of polynomial Lyapunov functions allows us to obtain asymmetric and non-convex estimated DoA, reducing the conservativeness. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed approach.

palavras-chave

Palavras-chave

regional stabilizationstatic output feedbackpolynomial Lyapunov functionsdiscrete-time nonlinear systemstime-varying parameterspolytopic modeldomain of attractionrobust stabilizationlinear matrix inequalities

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