Lyapunov Stabilization for Short-Memory Fractional Systems via Event-Triggered Impulsive Control

Abstract

The Lyapunov stabilization problem for fractional systems using event-triggered impulsive control is studied based on the short-memory principle. This framework effectively reconciles the non-local memory effects of fractional operators with the instantaneous nature of impulsive actions. By adopting Lyapunov-based methods, sufficient conditions are deduced to guarantee uniform stability and global asymptotic stability of the resulting closed-loop system. The proposed event-triggering mechanism explicitly incorporates the system order, extending the integer-order formulation and further enlarging the inter-impulse intervals. The theoretical results and control scheme are validated via a numerical example. Note to Practitioners—In real-time control applications like multi-agent coordination and networked systems, the plant often has memory-dependent dynamics, yet full fractional modeling is computationally heavy. The proposed short-memory event-triggered impulsive control balances fidelity and efficiency: it resets the fractional derivative at each impulse, compressing past memory into the current segment’s initial condition. This framework reconciles fractional nonlocality with instantaneous state resets, ensures uniform and global asymptotic stability, and enlarges inter-impulse intervals, something existing fractional event-triggered schemes cannot achieve. Moreover, embedding the system order explicitly into the triggering condition leads to fewer triggered events than in the integer-order case, thus reducing control cost.