Analytic and numerical stability of delay differential equations with variable impulses

Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

“…Motivated by [6], we give the following hypothesis. Hypothesis 3.1 Assume that the function α(t) satisfies:…”

“…In [6], X.Liu et al have shown the analytic and numerical stability results of a more general linear impulsive delay differential equation as follow:…”

“…T where r k ,r k , λ k ,λ k are real numbers, g i : R → {δ 1 2 , δ 2 2 } is a piecewise logical function as follows: 9) can be degraded into systems (7) or ( 8), then we can draw a conclusion that system ( 9) is more general than the systems in [4] and [6].…”

Exponential Stability for a Class of Linear Delay Differential Systems Under Logic Impulsive Control

“…From the perspective of the research topics on impulsive systems, in addition to periodic solutions [8], oscillation [9], noise [10], etc., various kinds of stability have also been studied extensively. For example, exponential stability [11], practical stability [12], interval stability [13], finitetime stability [14], numerical stability [15] and so on. From the perspective of the classification of impulsive systems, many research results have been reported for linear systems [9,11,13,16,17], nonlinear systems [18,19], functional differential systems [12,20,21], integro-differential systems [22], fractional differential systems [23,24] and so on.…”

“…From the perspective of the model composition of the impulsive system, due to the needs of practical problems, time-delay and stochastic effects are often taken into account in the impulsive model. Therefore, the delay impulsive systems such as [9,11,13,15,16,18,19,20,25,26], stochastic impulsive systems such as [27,28], and more complex stochastic delay impulsive systems such as [21,29] should be fully considered.…”