Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales

Vipin Kumar , Mohamed Djemai (1) , Michael Defoort (1) , Muslim Malik

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

In this article, we study the finite-time stability (FTS) and finite time stabilization problems for a class of switched impulsive systems evolving on an arbitrary time domain. This problem is formulated using time scale theory where the time domain can be continuous, discrete, union of disjoint intervals with variable gaps and variable lengths or any combination of these. Using common Lyapunov-quadratic and Lyapunov-like functions, we establish sufficient conditions to ensure the FTS results. Further, to solve the stabilization problem, we design state feedback controllers. We have illustrated the effectiveness of the obtained analytical results though numerical examples.

Domaines: Automatique / Robotique

Vipin Kumar, Mohamed Djemai, Michael Defoort, Muslim Malik. Finite-time stability and stabilization results for switched impulsive dynamical systems on time scales. Journal of The Franklin Institute, 2021, 358 (1), pp.674-698. ⟨10.1016/j.jfranklin.2020.11.001⟩. ⟨hal-03426314⟩