TY - JOUR
T1 - Necessary and Sufficient Conditions for Delay-Independent Stability of Linear Autonomous Systems
AU - Lewis, R. M.
AU - Anderson, Brian D.O.
PY - 1980/8
Y1 - 1980/8
N2 - Strict quasi-diagonal dominance of the system matrix is known to be sufficient for a linear autonomous system with arbitrary time delays in off-diagonal interactions to be stable. A small perturbation of the matrix yields a perturbed system with the same dominance, and, hence, stability properties. In this paper, it is shown that quasi-diagonal dominance is also necessary for stability with respect to small perturbations and arbitrary off-diagonal time delays. Weaker necessary conditions are given for systems which are themselves stable for all time delays, but which have perturbations that are unstable for certain delays.
AB - Strict quasi-diagonal dominance of the system matrix is known to be sufficient for a linear autonomous system with arbitrary time delays in off-diagonal interactions to be stable. A small perturbation of the matrix yields a perturbed system with the same dominance, and, hence, stability properties. In this paper, it is shown that quasi-diagonal dominance is also necessary for stability with respect to small perturbations and arbitrary off-diagonal time delays. Weaker necessary conditions are given for systems which are themselves stable for all time delays, but which have perturbations that are unstable for certain delays.
UR - http://www.scopus.com/inward/record.url?scp=0019046102&partnerID=8YFLogxK
U2 - 10.1109/TAC.1980.1102420
DO - 10.1109/TAC.1980.1102420
M3 - Article
AN - SCOPUS:0019046102
SN - 0018-9286
VL - 25
SP - 735
EP - 739
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -