Observer-based robust control of (0 < α < 1) fractional-order linear uncertain control systems

Stability and stabilisation problems for fractional-order linear (FOL) uncertain systems with fractional order alpha (0 < alpha < 1) are difficult and interesting. This study focuses on observer-based robust control for FOL uncertain system with fractional order 0 < alpha < 1. Recently, a new method based on linear matrix inequality is presented to solve the stability and stabilisation problems of FOL systems with fractional order 0 < alpha < 1. Based on the new method and the matrix's singular value decomposition, a necessary and sufficient condition for quadratic stability of observer- based FOL uncertain systems is presented in this study. Finally, two examples are given to illustrate the effectiveness of the proposed method.