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Integral transforms for a class of time-varying linear systems

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1 Author(s)
K. Narendra ; Harvard University, Cambridge, MA, USA

This paper presents an extension of the transform method to systems having parameters which vary with time. By using the general λ domain approach suggested by Zadeh for the analysis and synthesis of linear time-varying systems, a system function H(\lambda ) independent of time may be defined for the linear system. Such a system function has many of the advantages of that obtained for stationary systems using the Laplace transformation. By making H(\lambda ) a ratio of polynomials in the complex variable λ the pole-zero synthesis technique used for fixed systems may be applied to the time-varying case as well. Recently, a "building block" for the synthesis of a class of time-varying systems was suggested by Kilmer and Johnson. A similar building block for systems with exponentially varying coefficients is suggested in this paper.

Published in:

IRE Transactions on Automatic Control  (Volume:6 ,  Issue: 3 )