The finite-time stability of perturbed systems

Naim Zoghlami (1) , Lotfi Beji (1) , Mlayah Rhouma (2) , Azgal Abichou (2)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 LIM - Laboratoire d'Ingénierie Mathématique

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.

Keywords: Finite-time stable; Finite time stability; Averaging method; Average system; Lyapunov stability; Non-autonomous system; Nonautonomous; Perturbed systems; Stability method; Sufficient conditions; T-periodic; Time-varying perturbations

Domains: Automatic

Naim Zoghlami, Lotfi Beji, Mlayah Rhouma, Azgal Abichou. The finite-time stability of perturbed systems. IEEE Multi-conference on Systems and Control (MSC 2012), Oct 2012, Dubrovnik, Croatia. pp.1080--1085, ⟨10.1109/CCA.2012.6402364⟩. ⟨hal-00761641⟩