Stability analysis of impulsive stochastic differential systems in terms of two measures

Abstract

Stability, involving two measures, of a class of impulsive stochastic systems is investigated. Sufficient conditions for stability are obtained using Lyapunov-like functions and differential inequalities.

Comparison principle for stochastic delay impulsive systems with Poisson jump and Markovian switching

“…Our results are also regarded as the generalization and improvement of some known results, such as those in [20][21]. In [20], the authors established a comparison principle of existence and uniqueness and stability of solutions for stochastic impulsive systems.…”

“…Remark 1:The above problem is different from the previous results in [19][20][21], firstly, we study the more complex system model, i.e. SDIS with passion jump and Markov jump, which never haven't study it's stability via comparison approach.…”

“…In [20], the authors established a comparison principle of existence and uniqueness and stability of solutions for stochastic impulsive systems. The reference [21] extended two measures stability notations to stochastic impulsive differential systems and obtained sufficient conditions for the stability in terms of two measures. These results are both obtained via the comparison approach which is an interesting and efficient method for the complex dynamic system [22][23].…”

Stability of impulsive stochastic functional differential systems in terms of two measures via comparison approach

“…In recent years, stochastic effect to the stability of impulsive differential systems (IDSs) and IFDSs has attracted great interest of many researchers. Consequently, several interesting results on impulsive stochastic differential systems (ISDSs) and impulsive stochastic functional differential systems (ISFDSs), including impulsive stochastic delay differential systems (ISDDSs), have been reported [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

“…In particular, by employing Lyapunov-like function method and comparison principle, [10] obtained some sufficient conditions ensuring the existence, uniqueness and stability of solutions for ISDSs, and [11] investigated the stability in terms of two measures of ISDSs. Moreover, [12] and [13] applied comparison principle in chaos control.…”