Practical stability and attractors of systems with bounded perturbations

Alessandro Colotti (1) , Alexandre Goldsztejn (1)

1 LS2N - Laboratoire des Sciences du Numérique de Nantes

The classical Lyapunov analysis of stable fixed points is extended to perturbed dynamical systems that may not have any fixed point due to perturbations. Practical stability is meant here to assess the convergence of such systems. This is achieved by investigating a parametric optimization problem encoding some worst-case Lie derivative. Key properties of this parametric optimization problem are formulated. The proposed framework is finally applied to a class of perturbed linear systems tracking a highly nonlinear reference.

Keywords: Stability analisys; Lyapunov theory; Perturbed dynamical systems

Domains: Mathematics [math]; Dynamical Systems [math.DS]

Alessandro Colotti, Alexandre Goldsztejn. Practical stability and attractors of systems with bounded perturbations. 2022 IEEE 61st Conference on Decision and Control (CDC), Dec 2022, Cancun, Mexico. pp.5129-5134, ⟨10.1109/CDC51059.2022.9993324⟩. ⟨hal-03957165⟩