LMI-based Approaches To Model Reduction And Static Output Feedback Controller Design For Linear Systems

Due to the increasing development of informationization,systematization of the modern society,the dimensions of various control systems are becoming larger and larger, and the resulting complexity for system analysis and synthesis are also increased because the increasing order of the system model and the corresponding controller.Therefore, the reduction theory(i.e,model reduction and reduced-order controller design) is always a burgeoning research area.Great developments and wide applications have been made during the last several decades.However,there are still some problems that cannot be properly solved via the existing methods.For example,to some extent there exists inaccuracy and unreliability while using the existing method to cope with the known operating frequency information of the system,and there exists no approximation performance information over the known fiequency interval.Besides,how to reduce the conservatism of the existing LMI-based design methods for model reduction and static output feedback control is also an important problem.This thesis,based on previous works of others,presents new methods for model reduction and static output feedback control problems via LMI-based approach.For the model reduction problem that with known fiequency information about the input signal, the design conditions are developed with the aid of the generalized KYP lemma,which can deal with the approximation error over finite frequency directly.Therefore,the inaccuracy resulted by the existing methods such as frequency-weighted method can be avoided.For model reduction problems over entire frequency interval and static output feedback control problems for discrete-time systems,design methods with less conserv-ativeness compared with the counterpart ones in the literatures are developed.Besides, static output feedback controller design methods for systems with polytopic uncertainties and time-invariant delay are also presented respectively.Parts of the developed methods are applied to the model reduction of RLC circuit systems.Numerical examples and simulations illustrate the advantages and effectiveness of our approaches.Chapters 1-2 summarize the development and main research methods in the burgeoning research areas:model reduction and static output feedback control.Preliminaries about the considered problems are also given.Chapters 3-4 present new LMI-based design methods for H_{∞}and H₂ model reduction problems for linear continuous-time systems and discrete-time systems,respectively. Based on the recently developed generalized KYP lemma,design methods of H_{∞}model reduction are developed under low-frequency,middle frequency,high frequency,and entire frequency interval considerations according to the frequency information about input signal.Consequently,the uncertainty and unreliability of the existing methods for finite frequency model reduction problems are avoided.For the entire frequency H_{∞}model reduction problems,it is also pointed out that the conservativeness of the proposed methods in this chapter is less than the existing ones.Numerical examples and simulations illustrate the effectiveness and advantages of the proposed approach.Chapter 5 investigates the static output feedback control problem for linear discretetime systems.Stabilization,H_{∞}and positive real static output feedback control design methods are presented based on LMI technique respectively.By utilizing the parameter-dependent Lyapunov function method which originated in the research area of robust control and introducing more auxiliary variables,the conservativeness of the proposed methods is further reduced compared with the existing ones.Besides,the differences and relationships between the proposed methods and the existing methods can be clearly demonstrated due to those methods are presented in a unified framework in terms of the Finsler lemma.Numerical examples illustrate the effectiveness and advantages of the proposed approach.Chapter 6 focuses on the static output feedback control problem for linear discretetime systems with polytopic uncertainties.Firstly,robust positive realness analysis results are given based on the parameter-dependent Lyapunov function method and the relationship between the proposed result and the existing one is clarified theoretically.Combining some relaxation techniques,H_{∞}and positive realness static output feedback controller design methods are presented.Numerical examples illustrate the effectiveness and advantages of the proposed approach.Chapter 7 investigates the static output feedback control problem for linear discretetime systems with time-invariant state delay.Combining the Jensen inequality approach that dealing with the delay items,H_{∞}static output feedback controller design methods are presented.Numerical examples illustrate the effectiveness and advantages of the proposed approach.Finally,the results of the dissertation are summarized and further research topics are pointed out.