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 book combines two mathematical branches: dynamical systems and radial basis
functions. It is mainly written for mathematicians with experience in at least one of these two …

We propose a procedure for synthesizing piecewise linear optimal controllers for hybrid
systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in …

It is shown that for smooth nonlinear systems conditions for the existence of a Lyapunov
function that guarantees uniform exponential stability can be formulated as linear …

Contraction analysis considers the distance between two adjacent trajectories. If this
distance is contracting, then trajectories have the same long-term behavior. The main …

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 …

In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary
switched dynamical systems\(\dot {\mathbf {x}}=\mathbf {f} _\sigma (t,\mathbf {x})\) …

This article deals with a special type of Lyapunov functions, namely the solution of Zubov's
equation. Such a function can be used to characterize the exact boundary of the domain of …

An algorithm that derives a linear program for an ordinary differential equation is presented,
of which a feasible solution defines a continuous piecewise affine linear Lyapunov function …