General solution of two-dimensional singular fractional linear continuous-time system using the conformable derivative and Sumudu transform

Abstract

The effectiveness of this paper lies in presenting a new solution for the singular fractional two-dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini–Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results.

Keywords:

• Double Laplace transform
• double Sumudu transform
• Fornasini–Marchesini models
• fundamental matrix
• singular systems

Mathematics Subject Classifications:

• 34H05
• 34K35
• 37N35
• 13P25
• 32W50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper presents research results of the ACSY-Team (Analysis & Control systems team) and of the doctoral training on the Operational Research from the Pure and Applied Mathematics Laboratory UMAB and Decision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by National Higher School of Mathematics (NHSM), University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems theory (PRFU Project Code C00L03UN270120200003).