Control a class of fractional-order systems with delay in a specified sector

This paper is concerned with the problem of designing fractional-order time-delay systems with closed-loop eigenvalues in a prescribed region of stability. The main idea is to convert the fractional-order systems with time-delays into an equivalent standard fractional-order systems without delays. At the first, we compute a state feedback matrix which assigns all the eigenvalues to zero, then by using the method based on similarity transformation and assign the eigenvalues to fractional-order systems without delays compute state feedback matrix in a sector of the complex plane. This method is achieved by implementing properties of vector companion forms. The proposed algorithm can be used for the placement of closed-loop eigenvalues in a specified sector in plane and can be employed for fractional-order linear systems with large-scale. Also, the considerations can be easily extended for two-dimensional (2D) and descriptor fractional-order systems. Also, simulation results are presented to demonstrate the effectiveness of the proposed method.