Generalized Lyapunov Exponents of Homogeneous Systems

Andrey Polyakov (1) , Sergiy Zhuk (2)

1 VALSE - Finite-time control and estimation for distributed systems
2 IBM Research - Ireland

The paper deals the method of Lyapunov exponents for a class of a generalized homogeneous systems. Homogeneous systems may have some sup-exponential and super-exponential grows. In this case, the method of Lyapunov exponents becomes non-informative, e.g. all Lyapunov exponents may equal to zero but the system is globally uniformly asymptotically stable. In this paper we propose an approach which allows us to analyze a behavior of such homogeneous systems by means of the method of Lyapunov exponents.

Domaines: Automatique

Andrey Polyakov, Sergiy Zhuk. Generalized Lyapunov Exponents of Homogeneous Systems. CDC 2019 - 58th IEEE Conference on Decision and Control, Dec 2019, Nice, France. ⟨hal-02285137⟩