Research On Stability Of Stochastic Systems Based On Event-triggered Control

Stochastic systems are a type of system that involves random variables,random processes,or random events,and their outputs are random.In recent years,stochastic differential equations have received widespread attention from scholars in various fields such as science and engineering.However,due to various factors,uncertainty is inevitable in the actual modeling process.Therefore,this paper investigates the inputto-state stability problem of stochastic time-delay differential systems with external disturbances and stochastic time-delay nonlinear impulsive systems with exogenous disturbances.Due to periodic time-triggered control,which can only control at fixed time intervals,it is impossible to predict and respond to real-time changes in the system state.This may result in the control system being unable to respond promptly to emergency situations or system failures.Additionally,periodic time-triggered control requires regular transmission of control signals,which consumes a lot of network bandwidth and communication resources.To reduce the frequency of feedback control signal transmission,we adopt event-triggered control strategies and event-triggered pulse control strategies to stabilize the proposed system.Eventtriggered strategy refers to a method where a system or application automatically triggers certain operations or responds to events based on specific conditions.Based on this idea,a new event-triggered mechanism is designed to reduce the burden of communication and controller updates while also ensuring performance requirements.The main research contents of this paper are as follows:(1)For random time-delayed differential systems,the input-to-state exponential mean square stability of the system is studied,which takes into account the practical application of the system and is more suitable for practical engineering applications.Considering the occurrence of Zeno behavior in the event-triggered scheme,the existence of a lower bound on the event-triggered interaction time interval is proven,effectively avoiding Zeno behavior.A feedback controller based on event-triggered control strategy is designed to ensure the input-to-state exponential mean square stability of the system.(2)For nonlinear random time-delayed impulsive systems,the input-to-state exponential mean square stability of the system is studied,where the pulse sequence of the nonlinear random time-delayed impulsive system is generated by some predesigned event conditions.Considering the occurrence of Zeno behavior in the eventtriggered scheme,the existence of a lower bound on the event-triggered interaction time interval is proven,effectively avoiding Zeno behavior.A feedback controller based on event-triggered control strategy is designed to ensure the input-to-state stability of the system.(3)The input-to-state mean square stability of a nonlinear stochastic timedelayed impulse system was investigated in this study.The impulse sequence of the nonlinear stochastic time-delayed impulse system is generated by some pre-designed event conditions.Considering the chattering behavior in the event triggering scheme,the existence of a lower bound for the event triggering interaction time intervals is proved to effectively avoid chattering behavior.A feedback controller based on an event-triggered control strategy is designed to ensure the input-to-state stability of the system.Compared to traditional periodic time-triggered control,the controllers designed in this paper are all based on event-triggered control strategies.The stability of the system is described using linear matrix inequalities,and the feedback gain matrix and event-triggering function parameters are jointly designed by solving the linear matrix inequalities.The stability of the system is rigorously proven using event-triggering conditions and Lyapunov functions.