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 …

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 …

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

Domain of attraction plays an important role in stability analysis and safety verification of
nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like …

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

An approach for computing Lyapunov functions for nonlinear continuous-time differential
equations is developed via an alternative Yoshizawa-type construction. This construction is …

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 …

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 …

The asymptotic stability and global asymptotic stability of equilibria in autonomous systems
of differential equations are analyzed. Conditions for asymptotic stability and global …