Observer-based robust control of <i>a</i> (1≤ <i>a</i> &lt;2) fractional-order uncertain systems: a linear matrix inequality approach

Abstract

The study is concerned with a method of observer-based control for fractional-order uncertain linear systems with the fractional commensurate order a (1≤a&lt;2) based on linear matrix inequality (LMI) approach. First, a sufficient condition for robust asymptotic stability of the observer-based fractional-order control systems is presented. Next, by using matrix&apos;s singular value decomposition and LMI techniques, the existence condition and method of designing a robust observer-based controller for such fractional-order control systems are derived. Unlike previous methods, the results are obtained in terms of LMIs, which can be easily obtained by Matlab&apos;s LMI toolbox. Finally, a numerical example demonstrates the validity of this approach.