This book presents a modern and self-contained treatment of the Liapunov method for
stability analysis, in the framework of mathematical nonlinear control theory. A Particular …

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 provide a systematic investigation of using physics-informed neural networks to compute
Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) …

Many natural and artificial systems and processes encompass several modes of operation
with a different dynamical behavior in each mode. Switched systems provide a suitable …

A procedure for the numerical approximation of high-dimensional Hamilton--Jacobi--
Bellman (HJB) equations associated to optimal feedback control problems for semilinear …

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 method to compute invariant subsets of the region-of-attraction for
asymptotically stable equilibrium points of polynomial dynamical systems with bounded …

This book provides an approach to the study of perturbation and discretization effects on the
long-time behavior of dynamical and control systems. It analyzes the impact of time and …

Lyapunov's second or direct method is one of the most widely used techniques for
investigating stability properties of dynamical systems. This technique makes use of an …

Estimating the Domain of Attraction (DA) of equilibrium points is a problem of fundamental
importance in systems engineering. Several approaches have been proposed for the case …