The output feedback control synthesis for a class of singular fractional order systems

This paper investigates the output feedback normalization and stabilization for singular fractional order systems with the fractional commensurate order α belonging to (0,2). Firstly, an effective criterion for the normalization of singular fractional order systems is given with output differential feedback. Afterwards, both static and dynamic output feedback stabilization of such normalized fractional order systems are derived. Besides, the robustness to the parameter uncertainty and the initial conditions are discussed in detail. All the results are given via linear matrix inequality (LMI) formulation. Finally, three numerical examples are provided to demonstrate the applicability of the proposed approaches.