Related papers: Flatness of Discrete-time Systems, a simple Approa…
We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
Given an essentially finite type morphism of schemes f: X --> Y and a positive integer d, let f^{d}: X^{d} --> Y denote the natural map from the d-fold fiber product, X^{d}, of X over Y and \pi_i: X^{d} --> X the i'th canonical projection.…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…
We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
The possibility of operating in remote environments using teleoperation systems has been considered widely in the control literature. This paper presents a review on the discrete-time teleoperation systems, including issues such as…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as…
Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison,…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…