An Alternative Admissibility Theorem for Singular Fractional Order Systems

This work is concerned with the issue of admissibility for singular fractional order systems (FOS) with the fractional order 1 ≤ α <; 2. Firstly, an admissibility equivalence theorem is presented to establish a bridge between singular FOS and corresponding integer order systems. Then, an alternative necessary and sufficient condition for singular FOS different from existing results is developed. In this new criterion, singular matrix E is included in matrix inequality, which can better deal with the issue of stabilization for singular systems with uncertainty matrix E. Moreover, generalized Lyapunov equation of singular FOS is established, which is equivalent to the proposed alternative admissibility criterion. Finally, two numerical examples are presented to illustrate the effectiveness of main results in this paper.