Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

Abstract

In this article, by using Razumikhin-type technique, we investigate pth moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several stability theorems of impulsive hybrid stochastic functional differential equations are derived. It is assumed that the state variables on the impulses can relate to the finite delay. These new results are employed to a class of n-dimensional linear impulsive hybrid stochastic systems with bounded time-varying delay. Moreover, an effective M-matrix method is introduced to study the exponential stability of these hybrid systems. Meanwhile, some examples and simulations are given to show our results.

Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach

“…In this article, we will further study the stability of hybrid stochastic differential systems with delayed impulses by average impulsive interval approach and Lyapunov function method. The obtained results theoretically and numerically prove to be less conservative and more convenient to be applied than those Razumikhin‐type conditions in . It should be mentioned that this paper is enlightened in part by the works of Wu et al about exponential stability of impulsive stochastic delay differential systems.…”

Delay-dependent stability criteria for neutral-type neural networks with interval time-varying delay signals under the effects of leakage delay

“…Comparing the results listed in Table 2 with those in the recent literature, we crisply see that the proposed results have less conservatism in this example. Therefore, the resulting stability criterion in this paper is truly much better than those of [9,[11][12][13]16]. With F 1 = diag{0, 0, 0, 0}, by solving LMIs in Corollary 3.3, the purpose of this example is to calculate the MADBs of τ 2 such that the considered delayed system (56) is asymptotically stable for given τ 1 and μ.…”

“…Recently, much progress has been achieved in the study of NNs with time delays [1][2][3]. It is well known that, according to dependence on the size of the delays, the stability criteria are usually classified into two types, the delay-independent stability criteria [6,7] and delaydependent stability criteria [8][9][10][11][12][13][14][15][16]. As a result, the delay-dependent stability criteria have received much attention from the researchers because they are concerned with the size of the delay and provide less conservative results than delay-independent criteria.…”

“…For this case, the stability criteria for dynamical systems proposed in [29,30] cannot be applied because those results could not consider the case where lower bound of delay is nonzero. Therefore, it is of significant importance to study the stability of NNs containing a nonzero lower bound of the interval time-varying delays, and some of the researchers have reported fruitful results in the previous literature (see [8][9][10][11][12][13]16]). Recently, in [8], the asymptotic stability for a class of cellular NNs with interval time-varying delay was studied by combining novel LKFs and delay partitioning approach.…”

“…Recently, the asymptotic stability of delayed NNs have been extensively investigated in [10], where an improved delay-partitioning idea is employed. Very recently, in [13], the exponential stability criteria for cellular NNs with interval time-varying delays were proposed, based on the generalized activation functions. More recently, the authors in [11,12] investigated the delay-dependent stability criteria for NNs with interval timevarying delays via an augmented LKF and RCC approach.…”