Lyapunov Stability Theory for Caputo Fractional Order Systems: The System Comparison Method

The comparison method is the other method than the Lyapunov direct method in Lyapunov stability theory. Due to the long lack of the system comparison principle for Caputo fractional order systems, the corresponding system comparison method still remains blank. In this brief, we formally state and prove the system comparison method for Caputo fractional order systems, and illustrate it by an example with numerical simulations.