arXiv subjects

V Andrieu

Publications and source records attributed to V Andrieu.

2 recordsLinked to original sources

arXiv2015

Lyapunov functions obtained from first order approximations

In this paper, we study the construction of Lyapunov functions based on first order approximations. In a first part, the study of local exponential stability property of a transverse invariant manifold is considered. This part is mainly a rephrasing of the result of [3]. It is shown with this framework how to construct a Lyapunov function which characterizes this local stability property. In a second part, when considering the global stability property of an equilibrium point it is shown that the study of first order approximation along solutions of the system allows to construct a Lyapunov function.

math.DS↗

arXiv2013

Stability analysis for a class of linear systems governed by difference equations

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular cases, necessary and sufficient conditions for exponential stability are established, for multivariable systems with commensurate or rationally independent delays. A discussion on robust stability is proposed, for parametric uncertainties and time-varying delays.

math.OC↗