Robust orbital stabilization: A Floquet theory–based approach
Sætre, Christian Fredrik; Shiriaev, Anton; Freidovich, Leonid B.; Gusev, Sergei V.; Fridman, Leonid M.
Journal article, Peer reviewed
Published version
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https://hdl.handle.net/11250/3017851Utgivelsesdato
2021Metadata
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Originalversjon
International Journal of Robust and Nonlinear Control. 2021, 31 (16), 8075-8108. 10.1002/rnc.5738Sammendrag
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.