pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

Abstract

Summary This paper investigates the pth moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some pth moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become pth moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results.

Exponential input‐to‐state stability of delay reaction‐diffusion systems

“…EISS asks the system state to decay with an exponential index for the initial value. Since the EISS can reflect the rate of convergence, it has attracted a lot of attention [27][28][29][30][31][32][33].…”

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

“…Besides, Zhao et al obtained some results with respect to stochastic ISS criteria for switched stochastic systems. For the ISS of discrete‐time impulsive (stochastic) system, please refer to other works …”

“…For the ISS of discrete-time impulsive (stochastic) system, please refer to other works. [18][19][20] Compared with the Krasovskii approach, the advantage of the Razumikhin approach is that it does not need to construct some complicated Lyapunov functionals. Although the Razumikhin theorems in the aforementioned literature can be used to determine the iISS and ISS for many impulsive stochastic functional differential equations, some of the conditions seem to be too restrictive.…”

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

“…Similarly, the notion of IOSS and iIOSS were originally introduced for continuous control systems 2,6 and then were extended for discrete control systems 7 and hybrid systems. [8][9][10] Note that ISS and iISS have been adequately studied for impulsive systems in other works [11][12][13][14][15][16][17] and the references therein. Nevertheless, the possibility of impulsive effects and time delay on IOSS, has not been well studied in the aforementioned works.…”