Stabilization of Nonlinear Uncertain Fractional Systems via Flexible Impulses and Applications to Chemical Lur’e and Chaotic Financial Models

This study establishes robust exponential stability and exponential stability criteria for nonlinear fractional-order systems with parametric uncertainties under flexible impulsive control. Novel concepts are introduced to characterize the non-fixed, state-adaptive nature of impulsive delays. The existence and uniqueness of the global piecewise continuous solution are rigorously proven using both an iterative continuation method and the Banach contraction principle. Leveraging a convex Lyapunov function approach and linear matrix inequalities, sufficient conditions for robust exponential stability and exponential stability are derived, explicitly revealing the interplay between the system’s fractional order. Unlike prior works constrained by fixed or strictly monotonic delays, our framework permits fully flexible impulse timing and delays, yielding less conservative and more general stability results. The theoretical findings are validated through two practical applications where the stabilization of a fractional chaotic financial model and a fractional Lur’e chemical reaction system, demonstrating the efficacy of state-dependent flexible impulses in achieving controlled, convergent dynamics.