Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …

The stability of an equilibrium point of a nonlinear dynamical system is typically determined
using Lyapunov theory. This requires the construction of an energy-like function, termed a …

Contraction analysis considers the distance between two adjacent trajectories. If this
distance is contracting, then trajectories have the same long-term behavior. The main …

We study the stability of an equilibrium of arbitrarily switched, autonomous, continuous-time
systems through the computation of a common Lyapunov function (CLF). The switching …

Lyapunov functions are an important tool to determine the basin of attraction of equilibria in
Dynamical Systems through their sublevel sets. Recently, several numerical construction …

In this paper, we explore the merits of various algorithms for polynomial optimization
problems, focusing on alternatives to sum of squares programming. While we refer to …

Given an autonomous discrete time system with an equilibrium at the origin and a
hypercube containing the origin, we state a linear programming problem, of which any …

This article proposes an approach to construct a Lyapunov function for a linear large-scale
periodic system. In this case, in contrast to various variants of small-gain stability conditions …

A Riemannian metric with a local contraction property can be used to prove existence and
uniqueness of a periodic orbit and determine a subset of its basin of attraction. While the …

We present a novel method to compute Lyapunov functions for continuous-time systems with
multiple local attractors. In the proposed method one first computes an outer approximation …