On input-to-state stability of impulsive stochastic systems

On the pth moment integral input‐to‐state stability and input‐to‐state stability criteria for impulsive stochastic functional differential equations

“…Huang and Mao considered the ISS for stochastic retarded systems with Markovian switching. Wu et al and Yao et al investigated the ISS for impulsive stochastic differential systems, which extended the correspondent results in the work of Ning et al Wu et al and Yao et al studied the iISS and ISS for impulsive stochastic systems with delays by applying the Krasovskii approach and Razumikhin approach, respectively. Recently, Peng and Deng used the average dwell‐time (ADT) approach to investigate the ISS for impulsive stochastic delayed systems.…”

Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

“…In studies [18][19][20], the unified AII condition (4) is utilized for stability analysis and control of non-delayed impulsive systems. In this paper, we extend this condition to impulsive systems with multiple discrete time-varying delays.…”

“…Remark 4. Inequality (21) means that the pth moment of the trivial solution of system (19) grows at most exponentially and the pth moment Lyapunov exponent should not be greater than −( d + c). In particular, if d + c > 0, the trivial solution of system (19) is pth moment exponentially stable.…”

“…Given the particular advantage, the AII concept has attracted much attention since being proposed and has been extended to networks with time delays . Very recently, the following condition, which can be regarded as a unified form of the AII condition, was utilized in : where μ and λ are a pair of arbitrary positive constants, is the decay coefficient of the Lyapunov function between any consecutive impulsive instants, and corresponds to the jump coefficient of the Lyapunov function at impulsive instants. As the signs of the constants c and d are uncertain, the condition actually unifies several different cases, and the AII condition can be viewed as its special cases.…”

“…Given the particular advantage, the AII concept has attracted much attention since being proposed and has been extended to networks with time delays [15][16][17]. Very recently, the following condition, which can be regarded as a unified form of the AII condition, was utilized in [18][19][20]:…”