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Steady-state frequency response for periodic systems

DSpace at IIT Bombay

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Title Steady-state frequency response for periodic systems
 
Creator SULE, VR
 
Subject frequency response
linear periodic systems
eigenfunction expansions
eigenvalue problems
 
Description This paper extends the concept of steady-state frequency response, well known in the theory of linear time-invariant (LTI) systems, to linear time-varying 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 non-negative 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 state-space 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. . .
 
Publisher PERGAMON-ELSEVIER SCIENCE LTD
 
Date 2011-08-26T15:01:33Z
2011-12-26T12:57:30Z
2011-12-27T05:42:10Z
2011-08-26T15:01:33Z
2011-12-26T12:57:30Z
2011-12-27T05:42:10Z
2001
 
Type Article
 
Identifier JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 338(1), 1-20
0016-0032
http://dx.doi.org/10.1016/S0016-0032(00)00067-3
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11349
http://hdl.handle.net/10054/11349
 
Language en