Explicit stability condition for delta fractional order systems with α∈(0,+∞)

Yiheng Wei; Shuaiyu Zhou; YangQuan Chen; Jinde Cao

doi:10.1016/j.isatra.2024.04.032

Explicit stability condition for delta fractional order systems with α∈(0,+∞)

ISA Trans. 2024 May 7:S0019-0578(24)00187-3. doi: 10.1016/j.isatra.2024.04.032. Online ahead of print.

Authors

Yiheng Wei¹, Shuaiyu Zhou², YangQuan Chen³, Jinde Cao⁴

Affiliations

¹ School of Mathematics, Southeast University, Nanjing 211189, China. Electronic address: neudawei@seu.edu.cn.
² School of Mathematics, Southeast University, Nanjing 211189, China.
³ School of Engineering, University of California, Merced, CA 95343, USA.
⁴ School of Mathematics, Southeast University, Nanjing 211189, China; Ahlia University, Manama 10878, Bahrain.

PMID: 38744609
DOI: 10.1016/j.isatra.2024.04.032

Abstract

This paper delves into the stability of time-advance delta fractional order systems, with a specific emphasis on the order range (0,+∞) rather than the conventional range (0,1). The delta Laplace transform is used to investigate the stability of the suggested system, and a mapping relation ρ=ss+1 is introduced. The explicit stability condition is provided, articulated in relation to a specific distribution of eigenvalues of the system matrix. To validate this condition, the paper establishes equivalence between the delta difference and the nabla difference. Furthermore, both quantitative and qualitative analyses are conducted on the range of the unstable region. Finally, the correctness of the developed results is validated by three examples.

Keywords: Delta Laplace transform; Delta fractional order systems; Stable analysis; Time advance.