In the present study, the definition of discrete Mittag–Leffler stability is derived to characterize convergence rule of the pseudostates for nabla discrete fractional-order dynamic systems. Applying the Lyapunov stability theory, some new criteria are proposed to determine asymptotic stability of the zero equilibrium. In addition, by applying fractional comparison principle, the results are extended from Caputo discrete fractional-order systems to Riemann–Liouville systems. Moreover, a useful inequality is proposed to further improve the availability of the presented methods. Finally, some meticulously designed simulations are provided to verify the correctness and practicability of the elaborated stability notions.

在本研究中，导出了离散Mittag-Leffler稳定性的定义，以表征nabla离散分数阶动态系统伪状态的收敛规则。应用李雅普诺夫稳定性理论，提出了一些新的准则来确定零平衡点的渐近稳定性。另外，通过应用分数比较原理，将结果从Caputo离散分数阶系统扩展到Riemann-Liouville系统。此外，提出了有用的不等式以进一步改善所提出方法的可用性。最后，提供了一些精心设计的模拟来验证精心设计的稳定性概念的正确性和实用性。