In this paper we propose tools which can be applied to the study of limit cycles in spacecraft such as satellites and satellite launchers. In particular we provide tools which are able to predict the main properties of a limit cycle arising in the Attitude Control System in terms of amplitude and frequency. We also give sufficient conditions ensuring the stability of the limit cycle by means of Floquet theory. Moreover we address the global stability for linear systems with multivalued nonlinear feedback in terms of LMI conditions and we apply them to limit cycle analysis.
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