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Any system of globally-minimal degree is said to be \emph{globally minimal}. Anderson \cite{anderson} provides an algebraic characterization of all realizations of all spectral factors as follows. Minimal realizations of $\mS$ are related to globally-minimal realizations of spectral factors of $\Psi$ by the following lemma.  \begin{lemma}[\cite{anderson}] \label{lemma:andlem} Let $(A,B_s,C,D_s)$ be a minimal realization of the positive-real matrix $\mS(s)$ of \eqref{Zdef}, then the system $(A,B,C,D)$ is a globally-minimal realization of a spectral factor of $\Psi(s)$, i.e., $\mW(s)$ if and only if the following equations hold:  \begin{equation} \label{eq:and}  \begin{aligned} \begin{align}  RA^T + AR &= -BB^T\\ -BB^T\nonumber\\  RC^T &= B_s - BD^T\\ BD^T\nonumber\\  2D_s &= DD^T  \end{aligned}  \end{equation} \label{eq:and}  \end{align}  \noindent for some positive-definite and symmetric matrix ${R\in \RR^{n \times n}}$.  \end{lemma}