By using the characteristics of Moore-Penrose inverse, Theorem 13 provides sufficient conditions for the solvability of DOFC design problem for singular fractional-order systems with fractional-order a belonging to 0 < [alpha] < 1.
The following theorem is proposed for the design of DOFC for singular fractional-order systems with fractional-order a belonging to 1 [less than or equal to] [alpha] < 2.
Moreover, if the above conditions in (41)-(42) are feasible, the system matrices of an admissible DOFC in the form of (3) are given by
Using Matlab/LMItool to solve LMIs in (30)-(31), we can get the DOFC parameters to be determined as follows:
By Definition 5, the obtained DOFC can asymptotically stabilize the singular fractional-order system with fractional-order [alpha] = 0.