Stability Analysis And Controller Design For Several Classes Of Time-delay Systems

With the development of network communication,computer technology and modern control theory,human life has entered the era of intelligence and information technology.At the same time,it has greatly accelerated the progress of communication systems,industrial control systems,chemical systems,etc.However,in the actual control systems,due to the influence of various factors,it is often accompanied by time delay in the operation process.This is called time-delay phenomenon,which generally exists and can not be ignored.It has a certain impact on the stability and other performance of the systems.Therefore,how to reduce the impact of time-delay have been widely concerned by scholars.Over the past few decades,in-depth research have been carried out and rich research results have been achieved,but many practical problems still need to be further explored.In this paper,the stability of several kinds of time-delay systems is studied,and the specific controller design scheme is given.In view of the above problems,this paper can divide into the following aspects:(1)The stability of a class of linear time-delay systems will be studied by the interval partition approach.The basic idea is to construct an appropriate Lyapunov functional,and to use the Wirtinger inequality approach for the derivative term of the functional.Firstly,the stability of a class of time-varying delay systems is analyzed,and the corresponding stability criterion is obtained.Secondly,based on interval division technology,the time delay interval is bisected for obtaining a less conservative stability criterion.Finally,corresponding numerical examples and simulation diagrams will be given to show the validity of the design method.(2)Due to many kinds of random factors are always existent in the practical engineering application of the systems,in order to analyze the stability of practical systems better,it is necessary to in-depth study the stability of stochastic systems.In this chapter,the stability of a class of systems with stochastic delay is analyzed on the basis of the previous chapter.Firstly,the time-delay systems with probability characteristics are transformed into stochastic systems,and the triple integral term is introduced into Lyapunov functional.Secondly,the derivative result of the functional is treated by the free weight matrix and the linear matrix inequality approaches,andthe exponential mean square stability criterion is given based on the stochastic stability theory.Finally,the validity of the stability criterion is verified by numerical examples and simulation diagrams in this chapter.(3)The first two chapters all use linear systems as research objects,but the actual operation of the systems always exist nonlinear characteristics.In order to solve this problem,the stability of a class of nonlinear stochastic time-delay systems is studied and the corresponding controller is designed by using the method of T-S fuzzy model based on the previous two chapters.In the research process,the original nonlinear time-delay system is transformed into a nonlinear stochastic time-delay system by introducing a random variable.The delay distribution dependent stability criterion is derived.Then based on the stability condition,the controller design scheme is given.Finally,numerical examples and simulation diagrams are used to verify the validity of the stability criterion and controller scheme.