Stability Analysis And Synthesis For Neutral Delay Systems

Time delay arises quite naturally in industrial and engineering systems,such as communication systems,biological systems,chemical systems and electrical networks.The existence of delay makes the system analysis and synthesis become more complicated and difficult.Meanwhile,delay is frequently a source of instability and performance degradation in many dynamic systems,and thus considerable attention has been paid to the research on the stability analysis and controller synthesis of time-delay systems.In recent years,considerable attention has been focused on the stability analysis of various neutral delay systems.The theory of neutral delay systems is of both theoretical and practical interest.For example,functional differential equations of neutral type are the natural models of fluctuations of voltage and current in problems arising in transmission lines.Also,the neutral systems often appear in the study of automatic control,population dynamics.Various analysis techniques such as Lyapunov technique,characteristic equation method,or state solution approach have been utilized to derive stability criteria for asymptotic stability of the systems by many researchers.As to the stability,however,the analysis and controller synthesis to the neutral systems have been received very little attention.There are many challenging problems that need to be solved.In this dissertation,we study robust stabilization and robust H_∞control problems for neutral delay systems,and the control problems based on observers.First,based on the two fundamental stability theorems of NFDE and sufficiently using the structure of uncertainties and linear matrix inequality technique,we presented the solvable conditions of robust stabilization and robust H_∞control problems for neutral delay systems,meanwhile,the corresponding schemes of controller designs are given. The results in this dissertation are all presented via state feedback.To stability criterion point,the results we presented by the delay independent case.Second,the control problems based on observers for two class neutral systems are studied.Finally, robust H_∞control problems based on observers are considered for a class of neutral systems.The solvable conditions to robust H_∞control problems are given in terms of the reconstructed state when the real states are not available.The most results of this dissertation are presented by means of LMIs.The key to this method is to express the control objectives,such as asymptotical stability,H_∞performance etc.,by means of LMIs,and to express the parameters of controllers in terms of the solutions to LMIs.Simulation results are given at the end of each chapter to show the validity of each result.