Searcharxiv⌕ Search

arXiv subjects

M. De La Sen

Publications and source records attributed to M. De La Sen.

5 recordsLinked to original sources
arXiv2012

Preliminaries on pseudo-contractions in the intermediate sense for non-cyclic and cyclic self-mappings in metric spaces

A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is proven that if the space is uniformly convex and the subsets are non-empty, closed and convex then all the iterations converge to a unique closed limiting finite sequence which contains the best proximity points of adjacent subsets and reduce to a unique fixed point if all such subsets intersect.

math.FA↗
arXiv2011

Feedback Stabilization of a Class of Perturbed Nonlinear Autonomous Difference Equations

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order that that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e. perturbation - free) difference equation plus an incremental controller which completes the stabilization in the presence of dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize the nominal difference equation and also the perturbed one under a smallness-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

math.DS↗
arXiv2010

Analysis of Caputo linear fractional dynamic systems with time delays through fixed point theory

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate non-expansive or contractive self- mappings from initial conditions to points of the state- trajectory solution. The existence of a unique fixed point leading to a globally asymptotically stable equilibrium point is investigated in particular under easily testable sufficiency-type stability conditions. The study is performed for both the uncontrolled case and the controlled case under a wide class of state feedback laws.

math.DS↗
arXiv2010

On Chebyshev systems and non-uniform sampling related to controllability and observability of caputo fractional differential systems

This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order α . Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independent continuous functions or matrix functions, which are also Chebyshev systems, appear in such expansions in a natural way. Based on the properties of such functions, the controllability and observability of the Caputo fractional differential system of real order α are discussed as related to their counterpart properties in the corresponding standard system defined for α = 1. Extensions are given to the fulfilment of those properties under non- uniform sampling. It is proved that the choice of the appropriate sampling instants ion not restrictive as a result of the properties of the associate Chebyshev systems

math.DS↗