About the Stabilization of a Nonlinear Perturbed Difference Equation

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 than 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 perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-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.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Fiber Bragg Gratings, IT Techniques and Strain Gauge Validation for Strain Calculation on Aged Metal Specimens

This paper studies the feasibility of calculating strains in aged F114 steel specimens with Fiber Bragg Grating (FBG) sensors and infrared thermography (IT) techniques. Two specimens have been conditioned under extreme temperature and relative humidity conditions making comparative tests of stress before and after aging using different adhesives. Moreover, a comparison has been made with IT tecniques and conventional methods for calculating stresses in F114 steel. Implementation of Structural Health Monitoring techniques on real aircraft during their life cycle requires a study of the behaviour of FBG sensors and their wiring under real conditions, before using them for a long time. To simulate aging, specimens were stored in a climate chamber at 70 degrees C and 90% RH for 60 days. This study is framed within the Structural Health Monitoring (SHM) and Non Destructuve Evaluation (NDE) research lines, integrated into the avionics area maintained by the Aeronautical Technologies Centre (CTA) and the University of the Basque Country (UPV/EHU).