Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems†

1 December 1972

journal article
research article
Published by Taylor & Francis in International Journal of Control

Vol. 16 (6) , 1083-1100
https://doi.org/10.1080/00207177208932341

Abstract

Necessary and sufficient conditions of pointwise completeness at time t₁ (i.e. no component of the n-dimensional state vector should be equal to zero at time i, for all possible choices of the initial functions) of any system of the form x(t)= Ax(t) + Bx(t-h) are given. It has been shown that if the linear time-invariant delay-differential system is not pointwise complete at time t₁, then it is also not pointwise complete at time t>t₁ and if the linear time-invariant delay-differential system is not pointwise complete at time t=t₁ >(n-1)hthen it is also not pointwise complete at time t= >(n-1)h.

Keywords

This publication has 2 references indexed in Scilit:

On the Controllability of Delay-Differential Systems
SIAM Journal on Control, 1967
Differential-Difference Equations
Physics Today, 1963