Simple uniform exponential stability conditions for a system of linear delay differential equations

New exponential stability conditions for linear delayed systems of differential equations

“…The aim of the paper is to improve all the results of [8] and replace the constant 1 by the constant 1 + 1/e not only on the right-hand side of inequality (1.8), but in all explicit stability conditions derived in [8]. The only limitation in this paper in comparison with paper [8] is the condition a…”

“…Assume that there are constants The stability conditions derived in the paper are written in the form of inequalities with the right-hand sides which are equal the constant 1 + 1/e. As we mentioned in the introduction, the purpose of this paper was to improve all the results of [8] with the extra condition (1.9). The first open problem is to remove this condition in all statements of this paper.…”

“…As noted in [8], only few necessary stability conditions are known for systems. One of the interesting problems is the following.…”

“…Since this condition does not necessarily hold for equations considered in [8], all results of this paper and in [8] are independent. Our approach is based on estimates of the fundamental solution for scalar delay differential equations and on the Bohl-Perron type result.…”

“…Our approach is based on estimates of the fundamental solution for scalar delay differential equations and on the Bohl-Perron type result. Some ideas and schemes of [8] are utilized as well.…”