Exponential ultimate boundedness of impulsive stochastic delay difference systems. (English) Zbl 1390.93739
Summary: This paper is concerned with the exponential ultimate boundedness problems for the impulsive stochastic delay difference systems. Several sufficient conditions on the global \(p\)th moment exponential ultimate boundedness are presented by using the Lyapunov methods and the algebraic inequality techniques, and the estimated exponential convergence rate and the ultimate bound are provided as well. As an application, the boundedness criteria are applied to a class of discrete impulsive stochastic neural networks with delays. The obtained results show that the impulses not only can stabilize an unstable stochastic difference delay system but also can make an unbounded stochastic difference delay system into a bounded system. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 49N25 | Impulsive optimal control problems |
| 93C55 | Discrete-time control/observation systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
Keywords:
delay difference systems; exponential ultimate boundedness; impulsive control; stochastic effectsReferences:
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