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1 NON-A - Non-Asymptotic estimation for online systems Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 2 University of Leeds 3 UND - University of North Dakota Grand Forks 4 L2S - Laboratoire des signaux et systèmes

Abstract : The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a sign-indefinite function, which explicitly takes the systems- periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov 2013, 2015. The new result is established based on the framework of cell structure introduced in Leonov 1974 and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input.

Keywords : Input-to-state stability Periodic system Multistable system

Autor: Denis Efimov - Johannes Schiffer - Nikita Barabanov - Romeo Ortega -



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