A computing method on stability intervals of time-delay for fractional-order retarded systems with commensurate time-delays. (English) Zbl 1296.93175
Summary: This paper investigates the stability intervals of time-delays for fractional-order retarded time-delay systems. By the Orlando formula, the existence of the crossing frequencies is brought to verify the stability related to the commensurate time-delay. For each crossing frequency, the corresponding critical time-delays are determined by the generalized eigenvalues of two matrices constructed by the crossing frequency, the commensurate fractional-order and the coefficients of the characteristic function. The Root Tendency (RT) is defined to provide a method to analyze the number of the unstable roots for a given crossing frequency and critical time-delay. Based on the RT values and the number of the unstable roots for fractional-order systems with no time-delay, a computing method on the stability intervals of time-delay is proposed in this paper. Finally, a numerical example is offered to validate the effectiveness of this method.
MSC:
| 93D99 | Stability of control systems |
| 34A08 | Fractional ordinary differential equations |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 93B40 | Computational methods in systems theory (MSC2010) |
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