Lyapunov Stability Theory for Nonlinear Nabla Fractional Order Systems

Lyapunov method is a powerful tool for studying the stability of dynamic systems while existing work mainly focuses on the asymptotic stability and rarely concerns the boundedness. Under this background, this brief aims to discuss the boundedness of nonlinear nabla fractional order systems. By employing the nabla Laplace transform, two stability criteria in form of Lyapunov theorem are derived. Finally, two numerical examples are provided to evaluate the effectiveness and practicability of the theoretical results.