Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders

Bounded-input bounded-output stability conditions for fractional-order linear time-invariant (LTI) systems with multiple noncommensurate orders have been established in this paper. The orders become noncommensurate orders when they do not have a common divisor. Sufficient and necessary conditions of stability for a fractional-order LTI system with multiple noncommensurate orders are presented in two cases. Based on the numerical inverse Laplace transform technique, time-domain responses for a fractional-order system with double noncommensurate orders are presented to illustrate the obtained stability results.