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 …

Many existing tools in nonlinear control theory for establishing stability or safety of a
dynamical system can be distilled to the construction of a certificate function which …

This letter derives direct adaptive control algorithms for nonlinear systems nominally
contracting in closed-loop, but subject to structured parametric uncertainty. The approach is …

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

Three similar convergence notions are considered. Two of them are the long established
notions of convergent dynamics and incremental stability. The other is the more recent …

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 …

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 …