Analysis of periodic orbits based on uncertain data

A framework for robust stability analysis of periodic orbits of autonomous ordinary differential equations (ODE) is presented. The linearization of the dynamics around a periodic solution to an autonomous ODE has a neutrally stable mode. It is therefore not suitable to directly apply standard techniques for robustness analysis of time-varying systems. It is shown that the system can be transformed in such a way that the neutral mode can be removed from the stability analysis. Any method for robust stability analysis of periodically-varying linear systems can now be applied.