#7003. Robust orbital stabilization: A Floquet theory–based approach

December 2026publication date
Proposal available till 05-06-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Aerospace Engineering;
Mechanical Engineering;
Industrial and Manufacturing Engineering;
Electrical and Electronic Engineering;
Chemical Engineering (all);
Control and Systems Engineering;
Biomedical Engineering;
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Abstract:
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched- and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.
Keywords:
orbital stabilization; robust nonlinear control; sliding mode control; underactuated mechanical systems

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