Stabilization Of Fractional Order Uncertain Systems

It was find that many systems could be elegantly described with the help of frac-tional order system, such as aerospace, economy, biology and many other practical system models. As we all know, the problem of stability of fractional order systems is a very essential and crucial issue for control systems. The problem of stability have attracted increasing interest. However, due to various factors inevitably, prac-tical system models always coupled with uncertainty. Naturally, many theoretical results for regular systems have been extended to singular case. The most existing stability results for fractional-order systems are not applicable to analytical design of stabilizing controllers.Note that in most practical applications, the systems states are not completely accessible and all the designer knows are the output and input of the plant. In this case, the observer-based control or output feedback control is often needed. The main content of the thesis and the research results are as follows:This paper focuses on the stabilization for fractional-order uncertain linear sys-tems with the fractional commensurate order ?,0< ?< landl< ?< 2, re-spectively. Firstly, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are derived. Next, By using the matrix's singular val-ue decomposition(SVD)and linear matrix inequality (LMI) technics, The efficient approach are also presented for designing the observer and the state feedback con-troller for such fractional-order uncertain linear systems. Finally, numerical example demonstrates the validity of this approach.This paper focuses on the stabilization for fractional-order singular(FOS) un-certain linear systems with the fractional commensurate order 0< ?< 1. By using the matrix s singular value decomposition(SVD)and linear matrix inequality(LMI) technics, the sufficient conditions for robust state feedback stabilization based on the state observer are derived. The efficient approach are also presented for de-signing the observer and the state feedback controller under this condition. Finally, numerical example demonstrates the validity of this approach.