Direct Method for Stability Analysis of Fractional Delay Systems

Abstract

In this paper, a direct method is presented to analyze the stability of fractional order systems with single and multiple commensurate time delays. Using the approach presented in this study, first, without using any approximation, the transcendental characteristic equation is converted to an algebraic one with some specific crossing points. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Finally, the concept of stability is expressed as a function of delay. An illustrative example is presented to confirm the proposed method results.

Exact method for the stability analysis of time delayed linear‐time invariant fractional‐order systems

“…In other words, this method cannot detect stability windows of system in the delay space. Pakzad and Nekoui [26] have successfully generalised the direct method [27] for the stability analysis of FDS. A recent paper [28] extended the CTCR method to multiple time‐delayed fractional‐order system while the system also contains fixed time delays and has also been applied to FDSs with coefficient uncertainty and time delay uncertainty in [29].…”