The Problem Of Designing Static Output Feedback Controller And Filter For Fractional-order Systems

Recently, fractional-order control systems concerned as a new research field have caused considerable in systems control field. At present, the study of fractional order control systems is still its initial stages. The designing problem of controller for fractional order systems is still rarely. The paper studies the problem of designing static output feedback controller, filter for positive fractional continuous-time linear systems and observer-based H∞, state feedback con-troller for fractional continuous-time linear systems. The main contributions and achievements of this paper are detailed below:(1) The problem of designing the static output feedback controller for the positive fractional continuous-time linear systems with the fractional order a:the1≤α＜2case is investigated. Firstly, based on a system augmentation approach, a novel characterization on the stable con-dition of the closed-loop system is established. Then the designing method for static output feedback controller is presented. At last, a numerical example is shown to illustrate the feasibil-ity of the proposed method.(2) The problem of designing H∞filter for the positive fractional continuous-time linear systems with the fractional order a:the1≤α＜2case is investigated. Firstly, based on a system augmentation approach, a novel necessary and sufficient condition on asymptotically stable and H∞performance of the error system is established. Then the designing method for H∞filter is presented. At last, a numerical example is shown to illustrate the feasibility of the proposed method.(3) This problem of observer-based H∞state feedback controller for the fractional continuous-time linear systems with the fractional order a:the1≤α＜2case is investigated. A sufficient condition for the asymptotically stable and H∞performance of the close-loop system is pre-sented. Based on the matrix’s singular value decomposition method, An linear matrix inequal- ities algorithm to computer feedback gain matrix is presented. At last, a numerical example is shown to illustrate the feasibility of the proposed method.