Abstract: We introduce an algorithm for synthesizing and verifying piecewise linear Lyapunov functions to prove global exponential stability of piecewise linear dynamical systems. The Lyapunov ...

Abstract: This paper deals with piecewise-affine functions as Lyapunov function candidates for stability analysis of time-invariant discrete-time linear systems with saturating closed-loop control ...

This repository is the official implementation of Appendix D in the supplementary material of the paper, Improved Bounds on Neural Complexity for Representing ...

Multistability is a property necessary in neural networks in order to enable certain applications (e.g., decision making), where monostable networks can be computationally restrictive. This article ...

We consider piecewise H¹ functions and vector fields associated with a class of meshes generated by independent refinements and show that they can be effectively analyzed in terms of the number of ...