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# Controllability for linear singular systems on time scales

 Grant number: 14/15250-5 Support type: Research Grants - Visiting Researcher Grant - International Duration: September 11, 2014 - September 22, 2014 Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis Principal researcher: Jaqueline Godoy Mesquita Grantee: Jaqueline Godoy Mesquita Visiting researcher: Hernan R. Henriquez Visiting researcher institution: Universidad de Santiago de Chile (USACH), Chile Home Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil Associated research grant: 13/17104-3 - Impulsive functional dynamic equations on time scales and applications, AP.JP

Abstract

The main goal of this project is to investigate the controllability of singular systems on time scales. More precisely, we will study the system on time scales given by$$\left\{\begin{array}{lll}M x^{\Delta} (t) = Ax(t) + Bu(t), \vspace{2mm}\\y(t) = C x(t),\end{array}\right.$$where $x(t) \in \mathbb R^n$, $u(t) \in \mathbb R^m$, $y(t) \in \mathbb R^r$, $M, A \in \mathbb R^{n \times n}$, $B \in \mathbb R^{n \times m}$ and $C \in \mathbb R^{r \times n}$ are constant matrices and $M$ is a singular matrix. Also, we will investigate the existence of solutions for homogeneous and nonhomogeneous singular systems on time scales. We apply the variation of constants formula to characterize the controllability of singular control systems on time scales in terms of its parameters. (AU)