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 …

Numerous tasks in control systems involve optimization problems over polynomials, and
unfortunately these problems are in general nonconvex. In order to cope with this difficulty …

Invertible neural networks (INNs) are neural network architectures with invertibility by
design. Thanks to their invertibility and the tractability of their Jacobians, INNs have various …

We present a technique for learning control Lyapunov-like functions, which are used in turn
to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or …

We show that repulsive random variables can yield Monte Carlo methods with faster
convergence rates than the typical N^-1/2, where N is the number of integrand evaluations …

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 …

This paper presents LMI conditions for local, regional, and global robust asymptotic stability
of rational uncertain nonlinear systems. The uncertainties are modeled as real time varying …

The CPA method uses linear programming to compute Continuous and Piecewise Affine
Lyapunov functions for nonlinear systems with asymptotically stable equilibria. In [14] it was …

A Globally Asymptotically Stable Polynomial Vector Field with No Polynomial Lyapunov
Function Page 1 A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial …

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 …