Stability and Stabilization of Fractional-Order Uncertain Nonlinear Systems With Multiorder

Fractional-order (FO) commensurate systems have been widely studied in recent years, including their stability and control. However, for incommensurate FO systems these problems are still challenging and further research is needed. In this brief, the stability and stabilization of incommensurate FO nonlinear systems with time-varying bounded uncertainties are investigated. A new stability criterion in the form of linear matrix inequality is formulated by employing the FO comparison principle of multi-order FO systems. Then, a state feedback controller for system stabilization is derived based on the stability criteria proposed. Numerical simulations demonstrate the effectiveness of the theoretical formulation.