Necessary and sufficient admissibility condition of singular fractional order systems

This paper focuses on the admissibility analysis of singular fractional order systems. A novel stability criterion of normal fractional order systems is introduced first. An essential remark is provided on the distribution of eigenvalue of system matrix. Then a necessary and sufficient condition for the admissibility of singular fractional order systems is derived. All the results are obtained in terms of linear matrix inequalities. Finally, two illustrative examples are provided to validate the effectiveness of the proposed approach.