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Progressively better estimates of the domain of attraction for nonlinear systems via piecewise Takagi-Sugeno models: stability and stabilization issues. (English) Zbl 1378.93055

Summary: This paper introduces a novel approach for stability analysis and controller design of nonlinear models, both continuous- and discrete-time, based on an exact piecewise Takagi-Sugeno representation which generalizes the sector nonlinearity methodology. The motivation behind this work lies on the fact that piecewise-induced Takagi-Sugeno representations have smaller variations than single ones covering the whole modeling area, thus increasing the chances of finding piecewise solutions for stability analysis or controller synthesis. Moreover, this relaxation is shown to produce progressively better estimations of the domain of attraction via easy-to-implement algorithms that demand much less computational effort than other recent approaches in the literature. Examples are provided to highlight the advantages of the contributions over the existing methods.

MSC:

93C10 Nonlinear systems in control theory
93C42 Fuzzy control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Software:

SMRSOFT; PENBMI
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Full Text: DOI

References:

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