Explicit stability condition for delta fractional order systems with [formula omitted]

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.