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 …

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 …

We propose a subgradient algorithm for the computation of contraction metrics for systems
with an exponentially stable equilibrium. We show that for sufficiently smooth systems our …

The stability and basin of attraction of an equilibrium can be determined by a contraction
metric. A contraction metric is a Riemannian metric with respect to which the distance …

The numerical construction of Lyapunov functions provides useful information on system
behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is …

We show that contraction metrics for continuous time dynamical systems can be computed
numerically using numerical integration of certain initial value problems with a subsequent …

We show that for an ordinary differential equation (ODE) with an exponentially stable
equilibrium and any compact subset of its basin of attraction, we can find a larger compact …

The determination of exponentially stable equilibria and their basin of attraction for a
dynamical system given by a general autonomous ordinary differential equation can be …

Exponentially stable periodic orbits of ordinary differential equations and their basins' of
attraction are characterized by contraction metrics. The advantages of a contraction metric …