A stability criterion for fractional-order systems with α-order in frequency domain: The 1 < α < 2 case

Abstract

This paper proposes a stability criterion for linear fractional-order systems with the commensurate order α satisfying 1 <; α <; 2. The angle increment of the characteristic function in a linear fractional-order system is investigated, and the stability condition with respect to the angle increment is presented in the frequency domain. By this condition, we present a stability criterion to verify the stability of a linear fractional-order system according to the arrangement of the positive real solutions of two equations with respect to the coefficients of the characteristic function and the highest order. Finally, a numerical example is given to demonstrate the effectiveness of the proposed stability criterion.