Stability Analysis And H_∞ Control Of Time-varying Delay System

The time-delay phenomenon widely exists in new material technology,molecular engineering,controlled nuclear fusion technology,5G technology and clean energy technology.its existence has a great influence on some systems.If the influence is ignored,the system performance will deteriorate or even collapse.Therefore,it is of great significance to study time-varying delay systems.In this paper,the stability analysis,H_∞performance and control of variable Delay systems based on delay-product-type functional are discussed respectively.(1)Stability analysis of variable-delay systems is studied.First,based on the Lyapunov stability theory,a new single integral augmented Delay-product-type(DPT)functional with a delay-dependent matrix is constructed,which includes a delay-dependent matrix and an S-dependent integral term..In the process of analytic functional derivatives,a new integral inequality is used to deal with the integral term after time-delay division,and a less conservative stability criterion is obtained.Finally,the superiority of the method in this chapter is verified by a two-zone four-machine system,a typical second-order system and a single-machine infinite system.(2)The H_∞performance problem of the variable delay system is studied.The purpose of this chapter is to explore the role of DPT functional in reducing the conservatism of variable-delay systems compared to traditional Lyapunov functional.In order to make full use of time-delay boundary and derivative information,non-integral augmented DPT functional and triple integral augmented DPT functional are constructed based on the third chapter.In the process of analytic derivative,the integral term is processed comprehensively with the new integral inequality,so that the considered system remains asymptotically stable and satisfies the given performance index.Finally,the superiority of the method in this chapter is verified by a single-machine infinite system,a typical second-order system,a two-region four-machine system,and a perturbed variable-delay system.(3)The design of the H_∞controller of the variable-delay time-delay system is studied.The purpose is to explore an optimization method for time-delay systems that can effectively combine estimation techniques and L-K functional,so as to obtain controller existence conditions with less conservativeness.First,an LK functional including a new augmented vector and multiple integral terms is constructed;then,two more accurate inequalities are used to process the integral term after time-delay division,and a new one with less conservativeness is obtained.’s guidelines.On this basis,the controller is designed,and a linearization method is proposed,which transforms the design conditions of the H_∞controller into the form of strict linear matrix inequalities.Finally,the superiority of this method in typical second-order time-delay systems,variable-time-delay systems with disturbances and helicopter take-off and landing dynamic systems is verified by simulation.There are 6 figures,8tables,and 84 references in this paper.