In the space of finite-dimensional singular linear continuous-time-invariant systems described in the form 1 where , , , functional output-controllability character is considered. A simple test based in the computation of the rank of a certain constant matrix that can be associated to the system is presented.

The networked multi-agent systems that they are interconnected via communication channels have great applicability in multiple areas, such as power grids, bioinformatics, sensor networks, vehicles, robotics and neuroscience, for example. Consequently, they have been widely studied by scientists in different fields in particular in the field of control theory. Recently an interest has grown to analyze the control properties as consensus controllability and observability of multi-agent dynamical systems motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. In this paper, we analyze how to improve the control properties in the case of multiagent linear time-invariant dynamical systems.

Given a time series, running trends analysis (RTA) involves evaluating least squares trends over overlapping time windows of L consecutive time points, with overlap by all but one observation. This produces a new series called the ''running trends series,'' which is used as summary statistics of the original series for further analysis. In recent years, RTA has been widely used in climate applied research as summary statistics for time series and time series association. There is no doubt that RTA might be a useful descriptive tool, but, despite its general use in applied research, precisely what it reveals about the underlying time series is unclear and, as a result, its interpretation is unclear too. This paper contributes to such interpretation in two ways: 1) an explicit formula is obtained for the set of time series with a given series of running trends, making it possible to show that running trends, alone, perform very poorly as summary statistics for univariate time series and time series association; and 2) an equivalence is established between RTA and the estimation of a (possibly nonlinear) trend component of the underlying time series using a weighted moving average filter. Such equivalence provides a solid ground for RTA implementation and interpretation/validation. In this respect, the authors propose as diagnostic tools for RTA 1) the plot of the original series, with RTA trend estimation superposed, 2) the average R 2 value and the percentage of statistically significant running trends across windows, and 3) the plot of the running trends series with the corresponding confidence intervals.

AgradecimientosDurante el tiempo que he estado realizando esta tesis doctoral son muchas las personas que en mayor o menor medida han colaborado en ella, unas con su trabajo en la realización de las campañas de muestreo, otras con las tareas de laboratorio, algunas ayudando en el tratamiento de los datos y otras con su apoyo moral y paciencia.En primer lugar me gustaría agradecer a mi director Miguel Rodilla su papel como director de tesis no solo por sus conocimientos, ideas y duro trabajo en las campañas de muestreo, sino también por la labor de desbloqueo cuando las cosas no marchan como nos gustan. Ha sido un buen director de tesis así como un mejor compañero y excelente amigo.Por supuesto, a mis compañeros y amigos del equipo de investigación, Tania Morata,

We consider triples of matrices (E, A, B), representing singular linear time invariant systems in the form Eẋ(t) = Ax(t) + Bu(t), with E, A ∈ M n (C) and B ∈ M n×m (C), under proportional and derivative feedback.Structural invariants under equivalence relation characterizing singular linear systems are used to obtain conditions for controllability of the systems.