H_? Control Of Singular Fractional Order Systems

Fractional order systems are described by different equations with non-integer order.It has been found that the behavior of many physical systems can be more properly explained by fractional order systems than by integer order systems.For singular fractional order systems,because the singular form not only contains static information but also contains dynamic constraints,the singular linear system describes more accurately than the integer systems.In recent years,many scholars have studied integer order systems,and there has been abundant research results in this field.However,the research on fractional order systems and singular fractional order systems are still in their primary stage.This paper mainly studies the H? control problem of fractional order systems and singular fractional order systems.The contents are as follows:(1)The development and its research purpose and meaning of fractional order calculus are introduced.The current research status of the theory of fractional order systems and singular fractional order systems are given.Then the basic knowledge of theory of fractional calculus are introduced,separately including three basic functions commonly used in fractional order calculus:Mittag-Leffler function,Gamma function,Beta function.And three commonly used definitions:Grunwald-Letnikov definition(G-L definition),Riemann-Liouville definition(R-L definition)and Caputo definition and the relationship above them.(2)The issue of state feedback H? control of fractional order systems with the order 1<?<2 is studied by using linear matrix inequality(LMI)method and iterative LMI(ILMI)algorithm.Firstly,new necessary and sufficient conditions about stability of fractional order systems are proposed.On this basis,we put forward the new bounded real lemmas and design of state feedback controller of fractional order systems.Besides,we put forward the ILMI algorithm to solve the task of state feedback in this section.At last,we expand the conclusion to the state feedback H? control of fractional order systems.(3)H? control of singular fractional order systems with the order 0<?<1 is involved.The admissible criteria for H? control of singular fractional order systems as well as robust H? control of uncertain singular fractional order systems are presented by three different sufficient and necessary conditions in the form of LMI by using generalized KYP lemma.Theorems in chapter 4 and 5 have been put forward to solve the problems of H? control of singular fractional order systems and robust H? control of uncertain singular fractional order systems so that get more ideal results.(4)H? control of singular fractional order systems is studied,where 1<?<2.Firstly,Generalized bounded real lemma of fractional order systems is given.Then,necessary and sufficient conditions for state feedback H? control problem of singular fractional order systems is established.Finally,by using LMI Toolbox in Matlab to solver feasible solutions in this paper and to verify effectiveness of the conclusions.