Minimal set of generators of controllability space for singular linear dynamical systems

Due to the significant role played by singular systems in the form E ¿ x ( t ) = Ax ( t ) , on mathematical modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis of its structural and dynamic properties. However, much less effort has been devoted to studying the exact con- trollability by measuring the minimum set of controls needed to direct the entire system E ¿ x ( t ) = Ax ( t ) to any desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of columns, by making the singular system E ¿ x ( t ) = Ax ( t ) + Bu ( t ) controllable.Postprint (author's final draft

Functional output-controllability of time-invariant singular linear systems

In the space of finite-dimensional singular linear continuous-time-invariant systems described in the form \begin{equation}\label{eq1}\left . \begin{array}{rl} E \dot x(t)&= Ax(t)+Bu(t)\\ y(t)&=Cx(t)\end{array}{\kern-1mm}\right \}\end{equation} where $E,A\in M=M_{n}(\mathbb{C})$, $B\in M_{n\times m}(\mathbb{C})$, $C\in M_{p\times n}(\mathbb{C})$, 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 presentedPeer ReviewedPostprint (published version

Exploring Collaborative Work for the Creation of Interdisciplinary Units Centered on Intercultural Citizenship.

In this work we report on a collaborative project at a large Northeastern University, in which we explored how to best collaborate to develop interdisciplinary teaching units, which integrate intercultural citizenship (Byram, 2008) into world languages, mathematics and social studies sixth grade curricula. We argue for the importance of addressing current critical areas in education. After introducing a framework that allows teachers to focus on the development of intercultural citizenship while at the same time fostering skills in the diverse content areas, we report on how we worked with a group of graduate students, teachers and administrators in order to co-design interdisciplinary units focused on intercultural citizenship. An example of such an interdisciplinary unit is provided along with lessons learned about how we can facilitate this type of interdisciplinary collaboration. Our recommendations are based on qualitative analyses of the notes, memos and observations documented by the authors. Specifically, we share four emergent themes that illustrate how this group of educators successfully collaborated in this project: (1) Respecting disciplinary identities and boundaries, (2) Extending the understanding beyond the disciplines, (3) Ensuring a collaborative learning environment, and (4) Offering opportunities to continue the work beyond the course

Minimal set of generators of controllability space for singular linear systems

In recent years, there has been increasing the interest in the descriptive analysis of singular (also called generalized) systems in the form $E \dot x(t) = Ax(t)$ because they play important roles in mathematical modelling problems permeating many aspects of daily life arising in a wide range of applications. Considerable advances have been obtained in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the exact controllability measuring the minimum set of controls that are needed to steer the whole system $E \dot x(t) = Ax(t)$ toward any desired state. In this paper, we focus the study on the obtention of the set of all $B$ making the system $E \dot x(t) = Ax(t)+Bu(t)$ controllable