Robust orbital stabilization: A Floquet theory–based approach

The design of robust orbitally stabilizing feedback is considered. From a known controller for nominal, disturbance-free system, robustifying extension designed utilizing the sliding-mode control (SMC) methodology. main contribution paper to provide constructive procedure designing time-invariant switching function used in SMC synthesis. More specifically, its zero-level set (the sliding manifold) using real Floquet-Lyapunov transformation locally correspond an invariant subspace Monodromy matrix transverse linearization. This ensures asymptotic stability periodic orbit when system confined manifold, despite any uncertainties and external disturbances satisfying matching condition. challenging task oscillation underactuated Cart-Pendulum subject both matched unmatched disturbances/uncertainties demonstrates efficacy proposed scheme.