A relaxed characterization of ISS for periodic systems with multiple invariant sets

Denis Efimov (1, 2) , Johannes Schiffer (3) , Nikita Barabanov (4) , Romeo Ortega (5)

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

A necessary and sufficient criterion to establish input-to-state stability (ISS) of nonlinear dynamical systems, the dynamics of which are periodic with respect to certain state variables and which possess multiple invariant solutions (equilibria, limit cycles, etc.), is provided. Unlike standard Lyapunov approaches, the condition is relaxed and formulated via a sign-indefinite function with sign-definite derivative, and by taking the system's periodicity explicitly into account. The new result is established by using the framework of cell structure introduced in [24] and it complements the methods developed in [3], [4] for periodic systems. The efficiency of the proposed approach is illustrated via the global analysis of a nonlinear pendulum with constant persistent input.

Domaines: Automatique / Robotique

Denis Efimov, Johannes Schiffer, Nikita Barabanov, Romeo Ortega. A relaxed characterization of ISS for periodic systems with multiple invariant sets. 2016. ⟨hal-01351139⟩