Stability Analysis And Controller Design For A Class Of Stochastic Time-delay Systems

In recent years,the rapid development of modern control theory and computer science have promoted the progress of many research fields.Scholars have combined research disciplines with computer technology,gradually filling the blank chapters of the discipline.In the field of control,the current state of a system is not only related to the current time,but also affected by the previous one or many states.This phenomenon is called time delay phenomenon,and a system containing this phenomenon is called time-delay system.Normally,we can not ignore the existence of the phenomenon,because it is ubiquitous in our life.In some control systems,the existence of time delay is likely to be the main cause of the system not working.In the past decades,scholars have paid much attention to the time-delay system,and have conducted in-depth research on how to effectively reduce the impact of time-delay on the system.In this paper,based on the existing literature,taking the time-delay system as the starting point,considering the stochastic characteristics of the time delay and the nonlinear factors of the system,the stability problem and the controller design problem of the time-delay system are studied.The detailed work of this paper is as follows:(1)The stability of linear time-delay systems is studied.Firstly,based on the Lyapunov stability theory,the time-delay product terms and the augmented matrices were introduced to improve the Lyapunov-Krasovskii(L-K)functional.Secondly,a method based on auxiliary function inequality and extended convex combination method is used to deal with the integral terms in the process of functional derivation,and a less conservative stability criterion is given.Finally,the simulation results of examples are given.(2)In the process of studying the stability of linear time-delay system,it is found that the time delay has random characteristic,and such random factors will also have a certain impact on the performance of the system.The random variable with Bernoulli distribution is introduced to express the probability of the interval where the delay lies.In the derivation process of L-K functional,the idea of scaling is effectively used to estimate the boundary of the integral term in the derivation process,and then a system stability condition is given.Finally,the validity of the result is verified by numerical examples and simulation figures.(3)In practical systems,most systems have nonlinear factors.Therefore,this paper considers a class of nonlinear stochastic delay systems,describes the nonlinear system by T-S fuzzy model,and considers the influence of membership function on the stability criterion of the system,the stability of the described system is analyzed.Then,the nonlinear terms in the derivation process are processed by the contract transformation method,and the controller design scheme is derived.Finally,the simulation results of examples are given.