Stabilization of Stochastic Nonlinear Delay Systems With Exogenous Disturbances and the Event-Triggered Feedback Control

• Published in: IEEE transactions on automatic control Vol. 64; no. 9; pp. 3764 - 3771
• Main Author: Zhu, Quanxin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Control stability; Control systems; Delay; Delay systems; Discrete time systems; Disturbances; Event-triggered feedback control; Feedback control; input-to-state practically exponential mean-square stability; Linear matrix inequalities; linear matrix inequality (LMI); Lower bounds; Mathematical analysis; Matrix methods; Nonlinear systems; Stability criteria; Stabilization; State feedback; stochastic nonlinear delay system; Stochastic systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2882067

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.