On robust stability of sine-Gordon equation

Denis Efimov (1) , Emilia Fridman (2) , Jean-Pierre Richard (3)

1 VALSE - Finite-time control and estimation for distributed systems
2 Department of Electrical Engineering
3 Centrale Lille

A perturbed sine-Gordon equation is considered under the restrictions on the model parameters corresponding to the single equilibrium in the noise-free case. First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given. Second, the input-to-state stability property is investigated. The obtained theoretical results are illustrated by some simulations.

Domaines: Automatique / Robotique

Denis Efimov, Emilia Fridman, Jean-Pierre Richard. On robust stability of sine-Gordon equation. Proc. IEEE CDC, Dec 2019, Nice, France. ⟨hal-02418533⟩