## 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, ...).