On linear models for nonlinear systems
Best linear time-invariant (LTI) approximations are analyzed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an \(\ell_\infty\) signal setting. Applications to linear controller design, to identification of linear models and to the estimation of the size of the unmodelled dynamics are discussed.
scientific article; zbMATH DE number 1868216
scientific article