Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 85-92
Stability investigation of quadratic systems with delay
Kiev University, Department of Complex Systems Modelling, 64 Vladimirskaya Sreet, Kiev 252033, Ukraine
Received 1 January 1997; Revised 1 March 1999
Copyright © 2000 Vladimir Davydov and Denis Khusainov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Systems of differential equations with quadratic right-hand sides with
delay are considered in the paper. Compact matrix notation form is
proposed for the systems of such type. Stability investigations are
performed by Lyapunov's second method with functions of quadratic form.
Stability conditions of quadratic systems with delay, uniformly by
argument deviation, and with delay depending on the system's parameters
are derived. A guaranteed radius of the ball of asymptotic stability region
for zero solution is obtained.