A descriptor Takagi-Sugeno approach to frequency weighted nonlinear model reduction

In this note, the problem of frequency weighted nonlinear model reduction is addressed. It consists in approximating a given n^th-order nonlinear system by a k^th-order nonlinear system, where k < n. The goal is to compute the reduced order system minimizing the L2-gain from the input to the difference between the outputs of the original and the reduced systems. For this purpose the nonlinear system generating the approximation error is written under the descriptor Takagi-Sugeno formalism and is studied with the use of a multiple Lyapunov function, based on the descriptor approach. The obtained results are expressed in terms of Linear Matrix Inequalities (LMI) and the matrices defining the reduced order system are obtained as a result of LMI problem.