Relaxing the conditions of ISS for multistable periodic systems

Denis Efimov 1 Johannes Schiffer 2 Nikita Barabanov 3 Romeo Ortega 4
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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.
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Denis Efimov, Johannes Schiffer, Nikita Barabanov, Romeo Ortega. Relaxing the conditions of ISS for multistable periodic systems. IFAC 2017 - 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. ⟨10.1016/j.ifacol.2017.08.1365 ⟩. ⟨hal-01508766⟩

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