Robust Control and Stability Bound Analysis for a Class of LTI Fractional Order Uncertain Systems With 0 &#x003C; <inline-formula> <tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula> &#x003C; 1

Abstract

This paper concentrates on the robust control and maximal bound analysis of uncertainty for the LTI fractional order system (FOS), which is subjected to poly-topic and H-infinity bounded uncertainties with 0 <; α <; 1. Firstly, two problems including robust stability analysis and stabilization are investigated. Subsequently, the method of how to determine the maximal uncertainty bound of such system is discussed, and the corresponding linear state feedback stabilizing controller is obtained together. The conditions in terms of linear matrix inequalities (LMI) for these problems mentioned above are concluded as four theorems. Finally, the advantage of the proposed methods is illustrated by two numerical examples.

Keywords

• Fractional order system (FOS)
• H-infinity bounded uncertainty%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>-infinity bounded uncertainty
• maximal bound
• poly-topic uncertainty
• stabilization