Related papers: Notes on Contraction Theory
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
A class of peridynamic material models known as constitutive correspondence models provide a bridge between classical continuum mechanics and peridynamics. These models are useful because they allow well-established local constitutive…
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
This paper shows how the theory of adaptive observers can be effectively used in the design internal models for nonlinear output regulation. The main result obtained in this way is a new method for the synthesis of adaptive internal models…
A theory for kinetic arrest in isotropic systems of repulsive, radially-interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with…
A part of the theory of dislocations in crystals is revised with the aim to fit it into the framework of the nonlinear theory of plasticity initially designed for amorphous glassy materials.
We evaluate the loss of stability of axially compressed slender and thick-walled tubes subject to a residual stress distribution. The nonlinear theory of elasticity, when used to analyze the underlying deformation, shows that the residual…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
We discuss a recent effort in the modelling of binary component thin films, which yielded the same conclusions and stability limits as earlier work, despite a different method of incorporating constraints into the gradient dynamics…
In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…
We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus…
This manuscript contains technical details and proofs of recent results developed by the authors, pertaining to the design of nonlinear controllers from the experimental data measured on an existing feedback control system.