Nonlinear Impulsive Control for Stability of Fractional Systems

Abstract

This work investigates nonlinear impulsive control for short-memory fractional systems. A Lyapunov-based framework is developed to reconcile memory effects with instantaneous state jumps using fractional Dini derivatives and inequality techniques. Sufficient conditions are established for both asymptotic stability and finite-time contractive stability, with the system order explicitly embedded in the domain-of-attraction estimate and the reaching-time bound. For the former, the proposed nonlinear impulse-gain condition is less conservative, as it removes restrictive discrete-dynamics constraints compared with existing linear ones. For the latter, the finite-time contractive stability notion from the integer-order setting is extended to fractional impulsive systems, guaranteeing both finite-time entry into a prescribed target region and infinite-time boundedness thereafter, a property not discussed in existing fractional results. Two numerical simulations illustrate the theoretical findings.