## Welcome to ORBITADOR website!

ORBITADOR is a software tool for robustness analysis of dynamical systems commanded by differential equations. It implements a formal method to prove formally the stability of time-periodic systems and some other useful features.

## Key features

- Gives a simple condition of set inclusion which guarantees that the system is open-loop stable in the presence of perturbation when it is generating by periodic control that should be intrinsically robust or stable against possible perturbations or uncertainties.
- Proves the existence of a limit cycle (LC) of a dynamic system \(\Sigma\) and construct an enclosure of the LC which is an invariant set of \(\Sigma\). The method essentially consists in adding a small additive perturbation to \(\Sigma\), and finding an approximation \(T\) of the exact period such that the set of solutions of the perturbed system at the instant \((i+1)T\) is included in the set of solutions at \(iT\) for some integer \(i\).

## Analysis

This tool is tested in seveles known examples (Brusselator, Biped, Van der Pol system, ...).