In this paper we provide an overview of the state of tjhe art related to the study of the switched systems of differential equations. Such a panoramic study follows a bidirectional path. The first deals with the study of the considered systems of differential equations with regards the pooling of the same in two clusters, namely linear switched systems dependent on a continuous or discrete variable (such an independent variable usually represents time); and nonlinear switched and stochastic switched systems. The second direction deals with the study of these systems taking into account the more applied techniques to characterize 7066 Efrén Vázquez Silva et al. the stability and controllability thereof. We also have presented bidimensional switched systems.

ResumenEn el trabajo se hace una propuesta de algoritmo para la simulación de muestras poblacionales basado en los métodos de Monte Carlo y Bootstrap, cuando el tamaño de la muestra no es representativo para el universo estudiado. Tal necesidad es característica en las investigaciones de procesos o eventos cuyo intervalo de ocurrencia es muy amplio. En el trabajo se desarrolla un ejemplo a partir de datos reales recolectados de una máquina cosechadora a la cual se le calculó el índice de fiabilidad Vida Útil Gamma a uno de sus elementos hidráulicos. La implementación del algoritmo se desarrolló con el asistente matemático MATLAB y el diagrama de cálculos se muestra en el trabajo. Del análisis de los resultados se concluye que para investigaciones donde el tamaño de la muestra no sea representativa es útil aplicar la metodología propuesta para la estimación de las funciones de distribución necesarias y con ello estimar los intervalos de confianza de los indicadores buscados. Palabras clave: Índices de fiabilidad, método de Monte Carlo, muestra poblacional, simulación muestral. AbstractThis study proposes an algorithm to simulate population samples, supported by the Monte Carlo and Bootstrap methods, where the sample size is not representative of the universe being studied. This scenario is characteristic of investigation processes or events which span a long time period. This study developed an example with real-life data collected from a harvesting machine, calculating the lifetime reliability gamma index for a hydraulic element. The implementation of the algorithm was developed with the mathematical assistant MATLAB and the block diagram is shown at work. From the analysis of the results it is conclusive that, when the sample size being studied is very small, the proposed methodology is appropriate to estimate the necessary probabilistic distribution and therefore allows to estimate the confidence interval of the reliability index that is being sought.

The usage of solar trackers in solar energy technologies represents an alternative to increase the capture of solar radiation. However, the costs involved make it a prohibitive technology, having indexes and procedures that allow for its evaluation and determination of the viability of its use is of vital importance at the time of deciding its implementation and so to form the objective of this study. In the investigation carried out, the indexes of average gain, comparative efficiency and profitability are introduced and a procedure for the evaluation is developed, as a contribution to the decision-making process as to whether or not to use a solar tracker. It is confirmed that the use of trackers is completely viable when used with higher power technologies. Furthermore, it is shown that theoretically, the average gain index is higher than the values currently registered in scientific literature. Such factors support the possibility of designing and developing solar trackers with a higher gain, lower production costs and lower consumption indexes, as a way for their mass use in low power photovoltaic generators.

In this paper we obtain a method for the calculation the stability radius of the perturbed familyA is a Hurwitz-stable matrix; B = 0, C = 0 are given matrices specifying the structure of the perturbation, and ∈ R l×q represents the uncertainty of the perturbation. Mathematics Subject Classification: 34D20, 37C20, 34D10, 34D05