Stability analysis of time-delay incommensurate fractional-order systems

In this paper, the stability of time-delay incommensurate fractional-order systems is investigated. Using the Nyquist Theorem, a non-conservative condition is obtained that guarantees the stability of these systems. A formula is proposed which shows the delay values that break this stability condition. Using this formula associated with the assumption that the zero-delay system is stable, one can find the maximum allowable values for delay that guarantee the stability. The proposed method can be used for incommensurate fractional-order systems without any restrictions on fractional-orders or the system dimension. The effectiveness of the proposed method is investigated by applying it on the gene regularity network model. (C) 2022 Elsevier B.V. All rights reserved.