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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2009

Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions

Résumé

This paper provides finite dimensional convex conditions to construct homogeneous polynomially parameter-dependent Lur'e functions which ensure the stability of nonlinear systems with state-dependent nonlinearities lying in general sectors and which are affected by uncertain parameters belonging to the unit simplex. The proposed conditions are written as linear matrix inequalities parametrized in terms of the degree $g$ of the parameter-dependent solution and in terms of the relaxation level $d$ of the inequality constraints, based on algebraic properties of positive matrix polynomials with parameters in the unit simplex. As $g$ and $d$ increase, progressively less conservative solutions are obtained. The results in the paper include as special cases existing conditions for robust stability and for absolute stability analysis. A convex solution suitable for the design of robust nonlinear state feedback stabilizing controllers is also provided. Numerical examples illustrate the efficiency of the proposed conditions.
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Dates et versions

hal-00965332 , version 1 (27-03-2014)

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  • HAL Id : hal-00965332 , version 1

Citer

Vinícius F. Montagner, Ricardo C. L. F. Oliveira, T.R. Calliero, R. Borges, Pedro Luis Dias Peres, et al.. Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions. Nonlinear Analysis: Theory, Methods and Applications, 2009, 70 (5), pp.1803-1812. ⟨hal-00965332⟩
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