Stability Analysis And Control Methods Research For Interval Time Delay Systems Based On Lyapunov Functionals

With the rapid development of industrialization,the control system is becoming more complex.Some uncertain factors cannot be avoided,such as time-delay,disturbances and so on.They will affect the dynamic performance of the system in different level.In order to avoid unnecessary losses,we need to analyze more accurate mathematical models.Therefore,the research of time delay systems with disturbances or time-delay uncertainty has important theoretical meanings and practical value.Based on multiple integral forms of Lyapunov-Krasovskii(L-K)functionals and integral inequalities,this dissertation analyzes the stability of two kinds of interval time-delay systems with different disturbances via Lyapunov theory,and then analyzes the H? performance of a class of uncertain time-delay systems and designs the H? controller.The main contributions of this dissertation are summarized as follows:1.The stability analysis for a class of linear interval delay systems with nonlinear perturbations is discussed.Firstly,the new reciprocal convex combination lemma and auxiliary function type integral inequality are used to deal with the integral term in the L-K functional derivatives,which will further reduce the scope during the bounding process for integral terms.Then,a new L-K functional with multiple triple integral terms is constructed to improve the delay dependent stability criteria.2.The stability analysis for a class of interval uncertain time-delay systems is investigated.Firstly,the improved auxiliary Function-Based double and triple integral inequalities are introduced to further refine the estimation gap during the bounding process for integral terms,and consider the information on the double and triple integrals of system state.Then,the extended L-K functional is improved reasonably by adding triple integral augmented terms and quadruple integral terms.More delay information is considered,and the less conservative stability criteria is established.3.The H? performance analysis and H? control for time-varying delay systems with uncertain and external disturbance are studied.With the introduction of delay uncertainty,more general model of time delay system is established.Then,based on auxiliary Function-Based integral inequalities technique,which will further reduce the estimation gap during bounding process for integral terms and utilize the information on the double integrals of system state.Finally,an asymptotic stability criterion under disturbance rejection level ? is obtained via constructing an augmented L-K functional with delay lower bound information,and on this basis,the H? state feedback controller is designed.