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 …

We propose an automatic and formally sound method for synthesising Lyapunov functions
for the asymptotic stability of autonomous non-linear systems. Traditional methods are either …

This paper accompanies FOSSIL: a software tool for the synthesis of Lyapunov functions
and of barrier certificates (or functions) for dynamical systems modelled as differential …

Understanding the geometry of collision-free configuration space (C-free) in the presence of
Cartesian-space obstacles is an essential ingredient for collision-free motion planning …

We consider the problem of formally verifying almost-sure (as) asymptotic stability in discrete-
time nonlinear stochastic control systems. While verifying stability in deterministic control …

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a
challenging problem for real-world and industrial applications. Koopman operator theory …

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 …

Despite their spectacular progress, language models still struggle on complex reasoning
tasks, such as advanced mathematics. We consider a long-standing open problem in …

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

The equilibrium state of a dynamical system can be divided into the equilibrium point and
limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of …