Abstract
This paper is concerned with stability analysis of discrete-time stochastic delay systems with impulses. By using the sums average value of the time-varying coefficients and the average impulsive interval, two sufficient criteria for exponential stability of discrete-time impulsive stochastic delay systems are derived, which are more convenient to be applied than those Razumikhin-type conditions in previous literature. Both pth moment asymptotic stability and pth moment exponential stability are considered. Finally, two numerical examples to illustrate the effectiveness.
Highlights
Over the past decades, the impulsive phenomena have been intensively investigated since their significance and applications in areas such as economics, mechanics, chemical, biological phenomena, population dynamics, see other works and the references therein [1,2,3,4,5,6].On the other hand, time delays occur frequently in many evolution processes and it is the inherent feature of many physical processes
It is necessary to investigate the exponential stability for discrete-time stochastic systems with impulses
The analysis and synthesis problems for stability of discretetime impulsive systems have been extensively studied in recent years [24,25,26,27,28,29]
Summary
The impulsive phenomena have been intensively investigated since their significance and applications in areas such as economics, mechanics, chemical, biological phenomena, population dynamics, see other works and the references therein [1,2,3,4,5,6]. In [7], the authors have studied the pth moment exponential stability of a class of impulsive delay stochastic functional differential systems, by using the Lyapunov functions and Razumikhin techniques, some stability results have been given. In [20], the global exponential stability results for discrete-time delay systems with impulsive controllers have been considered. The analysis and synthesis problems for stability of discretetime impulsive systems have been extensively studied in recent years [24,25,26,27,28,29] Both of the above results require that the time delay in system is always greater than time delays in impulses, which leads to very conservative results.
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