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 …

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 …

In this paper, we explore the merits of various algorithms for polynomial optimization
problems, focusing on alternatives to sum of squares programming. While we refer to …

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 …

For planar piecewise affine systems, this paper proposes sufficient stability conditions based
on discontinuous Lyapunov functions. The monotonicity condition for discontinuous …

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 …

In this paper, we present a numerical algorithm for computing ISS Lyapunov functions for
continuous-time systems which are input-to-state stable (ISS) on compact subsets of the …

An integral part of the CPA method to compute Continuous and Piecewise Affine Lyapunov
functions for nonlinear systems is the generation of a suitable triangulation. Recently, the …

Recently the concept of essential neighbours of simplices was introduced for switched
systems and differential inclusions with triangulated state spaces. It was used to design an …

Continuous, piecewise affine (CPA) functions can be algorithmically parameterized to
deliver Lyapunov functions for compact invariant sets. We discuss flexible structures and …