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 introduces a numerical method to estimate the region of attraction for polynomial
nonlinear systems using sum of squares programming. This method computes a local …

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 …

We present a numerical algorithm for computing Lyapunov functions for a class of strongly
asymptotically stable nonlinear differential inclusions which includes spatially switched …

Given an autonomous discrete time system with an equilibrium at the origin and a
hypercube containing the origin, we state a linear programming problem, of which any …

Recently the authors proved the existence of piecewise affine Lyapunov functions for
dynamical systems with an exponentially stable equilibrium in two dimensions (Giesl and …

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 …

Lyapunov functions are an important tool to determine the basin of attraction of exponentially
stable equilibria in dynamical systems. In Marinosson (2002), a method to construct …

Estimating the domain of attraction (DA) of an equilibrium point is a long-standing yet still
challenging issue in nonlinear system analysis. The method using the sublevel set of …

In this article, two methods for constructing continuous and piecewise affine (CPA) feedback
stabilizers for nonlinear systems are presented. First, a construction based on a piecewise …