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Title:  Steadystate frequency response for periodic systems 
Authors:  SULE, VR 
Issue Date:  2001 
Publisher:  PERGAMONELSEVIER SCIENCE LTD 
Citation:  JOURNAL OF THE FRANKLIN INSTITUTEENGINEERING AND APPLIED MATHEMATICS, 338(1), 120 
Abstract:  This paper extends the concept of steadystate frequency response, well known in the theory of linear timeinvariant (LTI) systems, to linear timevarying systems with periodic coefficients, called periodic systems. It is shown that for an internally stable periodic system there exist complete orthogonal systems of real periodic functions {phi (n)} and {psi (n)} called eigenfunctions, such that for the inputs phi (n) every output of the system converges in steady state to sigma (n)psi (n), where sigma (n) are nonnegative real numbers. The set of all such numbers is called the singular frequency response of the system. In the case of LTI systems, the singular frequency response turns out to be consisting of the magnitudes of the sinusoidal frequency responses of the system. The singular frequency response {sigma (n)} is shown to be the singular spectrum of a compact operator associated with the system and has all the characteristics of the magnitude frequency response of LTI systems. A statespace realization of this operator and its adjoint leads to an alternative formulation of inverse of the singular frequency response as eigenvalues arising from a boundary value problem with periodic boundary values. (C) 2001 The Franklin Institute. . . 
URI:  http://dx.doi.org/10.1016/S00160032(00)000673 http://dspace.library.iitb.ac.in/xmlui/handle/10054/11349 http://hdl.handle.net/10054/11349 
ISSN:  00160032 
Appears in Collections:  Article

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