Static and dynamic output feedback stabilisation of descriptor fractional order systems

In this study, output feedback control is utilised to stabilise descriptor fractional order systems (FOS) with the fractional order α belonging to [1, 2) and (0, 1), respectively. Firstly, by the restricted equivalent transformations, a new necessary and sufficient condition of admissibility for descriptor FOS with 1 ≤ α < 2 is presented. Then, based on the methods of singular value decomposition, static and dynamic output feedback stabilisers of descriptor FOS with 1 ≤ α < 2 and 0 < α < 1 are obtained, respectively. Finally, four numerical examples are provided to verify the effectiveness of the proposed approaches.