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 …

This paper develops a new sampling-based method for stability verification of piecewise
continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system …

This article deals with a special type of Lyapunov functions, namely the solution of Zubov's
equation. Such a function can be used to characterize the exact boundary of the domain of …

An approach for computing Lyapunov functions for nonlinear continuous-time differential
equations is developed via a new, Massera-type construction. This construction is enabled …

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 …

Ordinary differential equations arise in a variety of applications, including eg climate
systems, and can exhibit complicated dynamical behaviour. Complete Lyapunov functions …

Dynamical systems describe the evolution of quantities governed by differential equations.
Hence, they represent a very powerful prediction tool in many disciplines such as physics …

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 …

We present a numerical technique for the computation of a Lyapunov function for nonlinear
systems with an asymptotically stable equilibrium point. The proposed approach constructs …

A strict Lyapunov function for an equilibrium of a dynamical system asserts its asymptotic
stability and gives a lower bound on its basin of attraction. For nonlinear systems, the explicit …