Stability of quaternionic systems: a determinantal approach

In this paper we propose a definition of determinant for quaternionic polynomial matrices. This definition is later used in the study of stability of linear quaternionic systems within the behavioral setting

Stability of quaternionic linear systems

The main goal of this paper is to characterize stability and bounded-input-bounded-output (BIBO)-stability of quaternionic dynamical systems. After defining the quaternion skew-field, algebraic properties of quaternionic polynomials such as divisibility and coprimeness are investigated. Having established these results, the Smith and the Smith-McMillan forms of quaternionic matrices are introduced and studied. Finally, all the tools that were developed are used to analyze stability of quaternionic linear systems in a behavioral framework

On the determinant of quaternionic polynomial matrices and its application to system stability

In this paper, we propose a definition of determinant for quaternionic, polynomial matrices inspired by the well-known Dieudonne determinant for the constant case. This notion allows to characterize the stability of linear dynamical systems with quaternionic coefficients, yielding results which generalize the ones obtained for the real and complex cases

Dynamical properties of quaternionic behavioral systems

In this paper we study behavioral systems whose trajectories are given as solutions of quaternionic difference equations. As happens in the commutative case, it turns out that quaternionic polynomial matrices play an important role in this context. Therefore we focus our attention on such matrices and derive new results concerning their Smith form. Based on these results, we obtain characterizations of system theoretic properties of quaternionic behaviors

Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure

In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant case in which the height, amplitude and period of the oscillations are all of the same order which is given by a small parameter $\epsilon > 0$. Applying an appropriate corrector approach we get strong convergence when we replace the original solutions by a kind of first-order expansion through the Multiple-Scale Method.Comment: to appear in Quarterly of Applied Mathematic

Global reachability of 2D structured systems

In this paper the new concept of 2D structured system is defined and a characterization of global reachability is obtained. This extends a well known result for 1D structured systems, according to which (A ,B ) is (generically) reachable if and only if the matrix [A B] is full generically row rank and irreducible

The disconnect between indicators of sustainability and human development

This paper presents an initial review of the theoretical and measurement discussions of sustainability and its relation to human development. As we show in this paper, there is an overall consensus about the importance of sustaining development and well-being over time, but in reality different development paradigms lead to different definitions and measures of sustainability. We review some of those measures, among which the Adjusted Net Savings (a green national accounting measure calculated by the World Bank and rooted in a weak concept of sustainability), the Ecological Footprint (calculated by the Global Footprint Network and rooted in a strong concept of sustainability, where environment is considered a critical resource), and the carbon dioxide emissions (a simple environmental indicator, used in international debate of climate change). Our analysis shows conflicting conclusions when studying the correlations between these indicators of sustainability and existing human development indicators, namely HDI, which emphasizes the need for further analysis to understand what “sustainable human development” means. Nevertheless, as we show here, over time there has been a close link between higher economic performance and energy consumption, which has been mostly based in the use of fossil fuels.sustainability, human development, measurement, energy.