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<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'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's LMI toolbox. Finally, a numerical example demonstrates the validity of this approach.

The paper deals with the forced oscillation of the fractional differential equation