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The Observer Designing Methods For Fractional Order Systems And Dissipative Problems For Fractional Order Singular Systems

Posted on:2017-03-03Degree:MasterType:Thesis
Country:ChinaCandidate:L N ZhangFull Text:PDF
GTID:2348330485950122Subject:Mathematics
Abstract/Summary:PDF Full Text Request
In practical engineering control field, many dynamical systems can be modeled by fractional order systems. Recently, fractional order systems have attracted considerable attention of many scholars and have made some achievements, but the research on the power properties and control comprehensive design has not been improved. On the basis of relevant theoretical research. this thesis will study the controller designing methods for the fractional order linear systems and the dissipative problems of the fractional order singular systems. The main contents of are detailed as follows(1) The problem of designing the observer for the interval fractional order linear systems i? investigated. Firstly, based on a system augmentation approach, a equivalent error system is established. Secondly, a novel sufficient condition on asymptotically stable is established combined with the system stability theory. Then the observer designing method is presented. At last, a numerical example is shown to illustrate the feasibility of the proposed method.(2) The problem of designing observer-based state feedback controller and the static output feedback controller for the fractional order linear systems is investigated. Firstly, based on the stability theory of the system, a novel sufficient condition on asymptotically stable is established by using the singular value decomposition method. Based on this, the controller designing method is presented. At last, a numerical example is shown to illustrate the feasibility of the proposed method.(3) The dissipative problems for the fractional order singular systems is investigated. Based on the generalized Kaiman-Yakubovic-Popov lemma and Elimination lemma, necessary and sufficient LMI conditions with equality constraints are presented to ensure the fractional order singular system is dissipative. Based on this, the results of bounded reainess and positive realness for the singular svstem are presented directly. At last, a numerical example is shown to illustrate the feasibility of the proposed method.
Keywords/Search Tags:Fractional order linear systems, Fractional order singular system, Observer- based state feedback controller, Static output feedback controller, Dissipativity
PDF Full Text Request
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