A graphical approach for stability and robustness analysis in commensurate and incommensurate fractional‐order systems

Abstract In this paper, a novel graphical approach for stability and robustness analysis in commensurate and incommensurate fractional‐order systems (FOS) is proposed. The approach can determine zero distribution of system characteristic equations with commensurate and incommensurate fractional‐orders in right‐half plane (RHP) and imaginary axis in the complex plane. The approach proposed is derived and generalizd from Routh‐type test for polynomials with the commensurate fractional and integer orders. In addition, the novel graphical approach can treat robustness issues of some certain systems. Furthermore, some examples are given to demonstrate the effectiveness of the approach. Finally, a proof is given to verify the correctness of the criterion.