Robust Stability and Stabilization of Commensurate Fractional Multi-Order Systems with Norm-bounded Uncertainties

This paper considers robust stability and stabilization problems of commensurate fractional multi-order systems with norm-bounded uncertainties. With the lowest fractional order
$0 < \alpha < 1$
, robust sufficient stability conditions are presented. Then depending on the accessibility of the systems' state vector and its fractional derivatives, a robust state feedback controller and a robust static output feedback controller are designed for stabilizing. All results are presented in the form of linear matrix inequality to take advantages of the LMI mathematical tools. Finally, numerical examples are implemented to demonstrate the effectiveness of the proposed results.