An error bound for model reduction of Lur´e-type systems

In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur´e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur´e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system.