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

Authors

1 Ph.D. Student, Math. Sci., Shahrood Univ., Shahrood, Iran.

2 Assoc. Prof., Math. Sci., Shahrood Univ., Shahrood, Iran.

3 Full. Prof., Math. Sci., Alzahra Univ., Tehran, Iran.

Abstract

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.

Keywords

Main Subjects

References

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Journal of Solid and Fluid Mechanics
Volume 9, Issue 3
October 2019
Pages 51-63

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