Stochastic stabilization of neutral stochastic delay systems based on discrete observations. (English) Zbl 1527.93465
Summary: This paper addresses the problem of stochastic stabilization for the neutral stochastic delay systems (NSDSs) based on discrete observations. Specifically, we design sampled-data based controllers (SDBCs) to stabilize NSDSs. To conquer the difficulties caused by the neutral term and stochastic stabilization, we introduce a new nominal system. By using the Lyapunov function method, we discuss the stability of the nominal system and provide a stability criterion. For the part of SDBC design, there are two methods: the lifting technique method (LTM) and the input delay method (IDM). The LTM is more effective for linear delay-free systems, but there is little research on the LTM for nonlinear stochastic delay systems. In this research, we combine the LTM with the equivalence technique for NSDSs, resulting in improved results. Additionally, to overcome the difficulty caused by LTM, we propose a series of mathematical tools, such as Gronwall’s inequality of the discrete version. We compared our method with the IDM presented in
[X. Mao, IEEE Trans. Autom. Control 61, No. 6, 1619–1624 (2016; Zbl 1359.93517)],
and our method performs better. Finally, to showcase the efficiency and correctness of our proposed approach, we provide an application.
MSC:
| 93E15 | Stochastic stability in control theory |
| 34K40 | Neutral functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 93C57 | Sampled-data control/observation systems |
Keywords:
neutral stochastic delay systems; sampled-data based controller; stochastic stabilization; lifting techniqueCitations:
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