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IMA Journal of Mathematical Control and Information 1988 5(2):147-166; doi:10.1093/imamci/5.2.147
© 1988 by Institute of Mathematics and its Applications
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A Generalized Frequency Response for Nonlinear Systems

S. P. BANKS and B. CHANANE

Department of Control Engineering, University of Sheffield Mappin Street, Sheffield S1 3JD

The principal aim of this paper is to present the idea of ‘generalized frequency response’ of a nonlinear input-output map Sxo. It is defined as {tau}{sigma} · Sxo · {tau}-1{sigma} where {tau}{sigma} is the canonical isomorphsim from the weighted space L2w[0, {infty}] to {ell}2 with respect to a given basis {sigma} for L2w(0 , {infty}) and the standard basis for {ell}2. Realization results are presented pertainig to the linear, bilinear, and nonlinear cases.


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