Begoña Cantó

Positive solutions of a discrete-time descriptor system

Discrete-time linear descriptor systems with restrictions over their trajectory are considered. In this work, some conditions required to achieve nonnegative output-response are studied. State–feedback and dynamic compensators are constructed to achieve the desired property. Finally, some applications to the Leontief economic model are given.

Positive N-periodic descriptor control systems ☆

This paper establishes the relationship between the positive N-periodic descriptor system in discrete-time and its associated invariant systems. Reachability and controllability properties of these kinds of systems are analyzed. Transmission of structural properties from the N-periodic system to their associated invariant systems is studied. Finally, some comments on the stability property are made.

Wavelet Transform application to the compression of images

In this paper a method for image compression is described. In the Wavelet Transform technique the coefficients below a certain threshold are removed. We propose a new type of global threshold to improve the wavelet compression technique. The aim is to maintain the retained energy and to increase the compression ratio with respect to other global thresholds commonly used.

Using the Wavelet Transform for T-wave alternans detection

This paper presents T-wave alternans (TWA) detection, applying the Wavelet Transform (WT) to electrocardiographic (ECG) synthetic signals. The TWA is generated with or without the sinusoidal addition of the wave with the required electrical level from 0.01 to 1 mV. The TWA is measured using the difference between the amplitudes of the augmented T-waves and the normal ones.

Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations

This paper presents the use of an iteration method to solve the identifiability problem for a class of discretized linear partial differential algebraic equations. This technique consists in replacing the partial derivatives in the PDAE by differences and analyzing the difference algebraic equations obtained. For that, the theory of discrete singular systems, which involves Drazin inverse matrix, is used. This technique can also be applied to other differential equations in mathematical physics.

Dynamic optimization of a gas-liquid reactor

A dynamic gas-liquid transfer model without chemical reaction based on unsteady film theory is considered. In this case, the mathematical model presented for gas-liquid mass-transfer processes is based on mass balances of the transferred substance in both phases. The identificability property of this model is studied in order to confirm the possible identifiable parameters of the model from a given set of experimental data. For that, a different modeled of the system is given. A procedure for the identification is proposed. On the other hand, the aim of this work is to solve the quadratic optimal control problem, using an explicit representation of the model. The problem includes some results on controllability, observability and stability criteria and the relation between these properties and the parameters of the model. Using the optimal control problem we study the stability of the system and show how the choice of the weighting matrices can improve the behavior of the system but with an increase of the energy control cost.

Structural identifiability of a model of dialysis

In this paper, structural identifiability from input-output data is considered. A mathematical model to describe a dialysis process based on linear dynamic systems is used and the identifiability of this model is tested. The problem of estimating the parameters and obtaining conditions to assure the uniqueness of the parameters is solved. Some conditions to obtain attractive points for the considered model are given, and finally, the stability problem is analyzed.

Structured parametric epidemic models

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ0 and the stability of the model in the equilibrium is studied using ℛ0 in terms of the model parameters.

A study on vaccination models for a seasonal epidemic process

In this paper seasonal epidemiological processes are considered and a strategy of periodic vaccination is proposed. The invariant formulations associated with an N-periodic system and the reproduction numbers associated with them are considered. A collection of measures to study the stability of the system is introduced. Moreover, the collection of s-basic reproduction number at time j help us to establish conditions on the periodic vaccination rates in the vaccination program. Finally, an SIR model is showed and a comparison between the results obtained using constant or periodic vaccination program is analyzed.

Drazin Inverse and Periodic Collection of Matrices

This paper is concerned with weakly