Explicit stability condition for delta fractional order systems with α∈(0,+∞)
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Updated: Jun 26, 2025

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
Published on: June 15, 2018
Yiheng Wei1, Shuaiyu Zhou1, YangQuan Chen2
1School of Mathematics, Southeast University, Nanjing 211189, China.
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.
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