Stability Analysis And Robust Control Of Several Types Of Stochastic Delay Systems With Multiple Delays

A stochastic system is a system that has some uncertain factors in the input and output or interference,that is,random factors.The state of the system is not constant,and may change with time.Its specific form depends on a certain period of time.This phenomenon It is called time-delay phenomenon,so the random system with time-delay phenomenon is called stochastic time-delay system.In the industrial field,the time-delay phenomenon of the system is more common,whether it is spacecraft launch and recovery,network identification,robot action There will be time delays in design,metallurgy,and pharmaceuticals,so that the system cannot accurately reflect the correct state in time,and the specific forms of various systems can be expressed by differential equations.In recent years,it has received extensive attention from scholars at home and abroad.According to this situation,for the stability of stochastic time-delay systems,this paper mainly uses the theoretical knowledge of Lyapunov theory,free weight matrix method,integral inequality and LMI method to explore.The contained hysteresis is extended to a more general case,and the integral term and nonlinear term are introduced to consider more forms of the system,making the system closer to practical applications and improving the practicability of the system.Based on these considerations,this paper specifically The research contents are as follows:1.Stability analysis of stochastic delay systems with based on two delays.Extend the stochastic delay system with one kind of delay to the stochastic delay system with both constant delay and variable delay.By constructing the Lyapunov functional,combined with the It(?) formula,the constructed function is processed,and then the integral is used.The derivative term is scaled by the inequality,and the sufficient conditions for the stability of the stochastic time-delay system are obtained,and on this basis,the robust control problem is explored,and finally it is verified by a numerical example.2.Stability analysis for multiple delay nonlinear stochastic systems.Research nonlinear stochastic systems with multiple delays and improve previous systems,extended to n terms,and nonlinear terms are added to obtain a nonlinear stochastic time-delay system,a new Lyapunov function is constructed,a free weight matrix is introduced,combined with the quadratic polynomial in the theory,obtain the corresponding matrix,apply linear matrix inequalities,establish new stability conditions,then add control input and controlled output terms,design a memoryless feedback controller,solve the robust H_∞ control problem of nonlinear stochastic time-delay systems,and finally use Numerical examples are used to verify.3.Research on the stability of a class of multi-delay neutral Lurie-type stochastic delay systems,constructs a new Lyapunov function,to handling nonlinear terms,and combined with the mean value theorem of integrals,adds auxiliary matrices to deal with the constructed functions,reduce conservatism,and obtain system stability conditions.A robust H_∞ feedback controller is designed to make the system satisfy the robust performance criterion,and finally,the validity of the theorem is verified by numerical examples.