The finite-time stability of perturbed systems

This paper deals with the finite-time stability of dynamic perturbed systems. The Lyapunov stability case is studied for nonautonomous systems and where the autonomous part is considered as finite-time stable and augmented by a separable function related to time-varying perturbations. As a result, the nonautonomous perturbed system is showed finite-time stable. Sufficient conditions are proposed for finite-time stability of homogeneous and T-periodic systems and where the averaging method has lead to a perturbed average system. The autonomous X4 flyer attitude and position stabilizations are obtained in finite-time. Some simulation results illustrate the proposed stability method.