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Stability of a chain of linear differential equations

By John R Dickerson and Paul A Erickson

Abstract

AbstractThe behavior of an infinite sequence of ordinary differential equations of the form: dXndt = ∑i=−MN LiXi+n, 0 ⩽ n, 0 < N, M < ∞, Xn(0) = Cn, (1) Xn ≡ 0, n < 0, where Xn(t) is a vector valued function of R+, is studied in spaces of infinite sequences of vectors. In particular, sufficient conditions for asymptotic stability of this sequence of linear equations are established and applied to the stability analysis of a string of vehicles with a simple form of automatic control

Publisher: Published by Elsevier Inc.
Year: 1974
DOI identifier: 10.1016/0022-247X(74)90004-3
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