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Article Dans Une Revue Linear Algebra and its Applications Année : 2015

A descriptor Takagi–Sugeno approach to nonlinear model reduction

Benoît Marx

Résumé

In this note, the problem of nonlinear model reduction is addressed. It consistsin approximating a givennth-order nonlinear system by akth-order nonlinearsystem, wherek < n. The goal is to compute the reduced order system min-imizing theL2-gain from the input to the difference between the outputs ofthe original and the reduced systems. For this purpose the nonlinear systemgenerating the approximation error is written under the Takagi-Sugeno formal-ism and is studied with the use of a multiple Lyapunov function, based on thedescriptor approach. The obtained results are expressed in terms of Linear Ma-trix Inequalities (LMI) and the matrices defining the reduced order system areobtained as a result of LMI problem. Uncertain nonlinear system reduction is also addressed.
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hal-01141264 , version 1 (17-04-2019)

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Benoît Marx. A descriptor Takagi–Sugeno approach to nonlinear model reduction. Linear Algebra and its Applications, 2015, 479, pp.52-72. ⟨10.1016/j.laa.2015.03.030⟩. ⟨hal-01141264⟩
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