On stability of linear time-invariant fractional order systems with multiple delays

An intriguing perspective is presented in studying the stability robustness of linear time invariant (LTI) fractional order systems with multiple time delays against delay uncertainties (this means that the time delays are constant but their true values are not exactly known). The new approach is based on a holographic mapping, which is implemented over the parametric space of the delays. This mapping considerably allays the problem, which is otherwise known to be notoriously complex. We show that this procedure analytically reveals all possible stability regions precisely in the space of multiple time delays. For simplicity of conveyance and without loss of generality, the number of time delays is taken as two in this document. As an added strength, it does not require the system under consideration to be stable for zero delays. An example case study is also provided to approve the proposed method results, which is not possible to analyze using any other methodology known to the authors.