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- Title
The Distributional Solution of the Fractional-order Descriptor Linear Time-Invariant System and Its Application in Fractional Circuits.
- Authors
Zaiyong Feng; MingZhong Chen; Linghua Ye; Lingling Wu
- Abstract
The distributional solution of the Fractional-Order Descriptor Linear Time-Invariant System (FODLTIS) and its application in the fractional circuits are studied. Based on proposing the definition of 0cDαt δ(t), the Laplace transform of 0cDαt δ(t) is investigated. Next, with regard to FODLTIS, the system is decomposed into fast subsystem and slow subsystem by restricted equivalent transformation. Solution for the slow subsystem is known. Using Laplace transform of 0cDαt δ(t), distributional solution for the fast subsystem is derived. Combining solutions of the slow subsystem and the fast subsystem, the distributional solution of FODLTIS is successfully obtained. The structure of the distributional solution of the system shows that the superposition principle for the system still holds for FODLTIS. Finally, the distributional solution of FODLTIS is applied in the fractional RC circuit, fractional RL circuit, and the fractional LC circuit with ideal operational amplifier. Numerical solution and figures are made to verify the correctness and stability of the solution.
- Subjects
LINEAR systems; OPERATIONAL amplifiers; SUPERPOSITION principle (Physics); RC circuits; CAPUTO fractional derivatives
- Publication
IAENG International Journal of Applied Mathematics, 2020, Vol 50, Issue 3, p172
- ISSN
1992-9978
- Publication type
Article