The robust stability and stabilization problems of uncertain fractional-order singularly perturbed systems are studied in this paper. The fractional order of the system is commensurate and satisfies \(0<\nu <1\) . Firstly, the sufficient conditions for the robust stability of the systems are derived, which take the form of linear matrix inequalities (LMIs). Secondly, the problem of controller synthesis is analyzed, and the state feedback controller is designed to stabilize the uncertain fractional-order singularly perturbed systems, and the sufficient conditions for stabilization are established in the form of bilinear matrix inequalities (BMIs). Thirdly, an LMI-based iterative algorithm is provided to solve these BMI-based conditions. Finally, the validity of the obtained conclusions is verified by two numerical examples.
