Observer-based robust control of a (1⩽ a ≪ 2) fractional-order uncertain systems: a linear matrix inequality approach

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.