We introduce a procedure to reveal invariant stable and unstable manifolds, given only experimental data. We assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle. We show that the method is able to capture the fine structure of the manifold, is independent o...

Methods to estimate the Hausdorff dimension of invariant sets of scattering systems are presented. Based on the levels' hierarchical structure of the time delay function, these techniques can be used in systems whose future-invariant-set codimensions are approximately equal to or greater than one. The discussion is illustrated by a numerical example of a scatterer built with four hard spheres l...

Robust stability and performance analysis techniques are presented for time-delay systems consisting of the feedback interconnection of a linear time-delay system, with a bounded and casual linear operator. This linear operator features all the parameter and/or dynamical uncertainties excluding the delay elements. The delays considered are noncommensurate, time-invariant but uncertain, residing...

A new singular impulsive delay differential inequality is established. Using this inequality, the invariant and attracting sets for impulsive neutral neural networks with delays are obtained. Our results can extend and improve earlier publications.

We show the construction of a rotationand reflection-invariant local function for a two-dimensional asynchronous cellular automaton with only 3 states and radius 1 Moore neighborhood in which one can implement arbitrary delay-insensitive circuits.

Let A be a finite or countable alphabet and let θ be literal (anti)morphism onto A∗ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short). We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin θ-invariant codes, maximality and complet...

The objective of this work is to study the benefits that delay can provide in simplifying the control process of largescale systems, motivated by the availability of different types of delays in man-made and biological systems. We show that a continuous-time linear time-invariant (LTI) controller can be approximated by a simple controller that mainly uses delay blocks instead of integrators. Mo...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.

This paper gives a new solution to the output feedback H2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized H2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finite-dimensional quadratic p...

Abstract: This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L1−performance analysis are given in terms of linear matrix inequalities (LMIs). Based on which, a dynamic output-feedback controller is then designed. All the ...