LMI-based stability analysis for piecewise multi-affine systems
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Universidade Federal de Minas Gerais
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This paper provides a computational method to study the asymptotic stability of piecewise multi-affine (PMA) systems. Such systems stem from a class of fuzzy systems with singleton consequents and can be used to approximate any smooth nonlinear system with arbitrary accuracy. Based on the choice of piecewise Lyapunov functions, stability conditions are expressed as a feasibility test of a convex optimization with linear matrix inequality constraints. The basic idea behind these conditions is to exploit the parametric expressions of PMA systems by means of Finsler's lemma. Numerical examples are given to point out the effectiveness of the proposed method.
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Sistemas difusos, Liapunov, Funções de, Sistemas não lineares
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Stability analysis , Fuzzy systems , Nonlinear systems , Numerical stability , Symmetric matrices , Lyapunov methods , Linear matrix inequalities, Fuzzy systems , linear matrix inequalities (LMIs) , piecewise Lyapunov functions , piecewise multi-affine (PMA) systems , singleton consequents , stability analysis, Stability Analysis , Effective Method , Numerical Examples , Nonlinear Systems , Class Of Systems , Stability Conditions , Lyapunov Function , Fuzzy System , Linear Matrix Inequalities , Arbitrary Accuracy , Stability Of System , Sufficient Conditions , Regular Grid , State-space Model , Conditions Of Theorem , Fuzzy Model , Fuzzy Control , Stability Analysis Of Systems , Numerical Solver , Piecewise Linear Model , Affine Systems , Quadratic Lyapunov Function , General Nonlinear Systems
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https://ieeexplore.ieee.org/abstract/document/7468468