A descriptor Takagi–Sugeno approach to nonlinear model reduction
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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