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LMI-Based Stability Analysis for Piecewise Multi-affine Systems

Abstract : 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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https://hal-uphf.archives-ouvertes.fr/hal-03428735
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Submitted on : Monday, November 15, 2021 - 11:46:32 AM
Last modification on : Tuesday, November 16, 2021 - 3:56:47 AM

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Tran Anh-Tu Nguyen, Michio Sugeno, Victor Campos, Michel Dambrine. LMI-Based Stability Analysis for Piecewise Multi-affine Systems. IEEE Transactions on Fuzzy Systems, Institute of Electrical and Electronics Engineers, 2017, 25 (3), pp.707-714. ⟨10.1109/TFUZZ.2016.2566798⟩. ⟨hal-03428735⟩

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