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/dokumenty/skolni/TDS/1uloha/reseni.tex
9,6 → 9,25
 
\begin{document}
 
\section{Řešení 1. zadané úlohy}
\section*{Řešení 1. zadané úlohy - Jakub Kákona}
 
\begin{enumerate}
\item Ano, systém je dynamický - jeho stav je funkcí času.
 
\item Systém je časově invariantní, neboť nemá žádnou časovou závislost, jeho výstup je pouze reakcí na vstupní stav. Systém je lineární, protože je definován na lineárních prostorech a relace systému je jejich podprostorem.
 
\item Systém není časově invariantní neboť je složenou funkcí času a proto není neměnný vůči časovému posunu.
Systém bude lineární, pokud je definován na lineárních prostorech U a Y.
 
\item Jde o diferenční systém (v diskrétním stavovém prostoru). Systém je typu IOM protože každému k přiřazuje unikátní výstup.
 
\item Stav systému může být popsán dvěma proměnnými. $x_1=u$ a $x_2=v$.
 
Stavové rovnice pak jsou tvaru
 
$\dot x_1 =x_2$, $\dot x_2 = x_1 - x_2$
\end{enumerate}
 
\end{document}