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Next: Remarks on Jordan Blocks Up: Triangular Input Balanced Realizations Previous: Gauss-Meixner Summation

Bidiagonal Representation of TIB Systems

The matrix of a single input-single output TIB system can always be written as a ratio of bidiagonal matrices. To fix ideas we consider the lower triangular case. We obtain
equation845
that is
eqnarray848
and
eqnarray868
where tex2html_wrap_inline1386 are the diagonal elements (eigenvalues) of A. Since A is stable, tex2html_wrap_inline1392, tex2html_wrap_inline1394 and M is nonsingular.

It follows that the realization
eqnarray121
can be implemented as the realization
eqnarray890
which is obviously tex2html_wrap_inline1320 in complexity. It is nice to know that tex2html_wrap_inline1400, which additionally simplifies things.




Fri Jun 27 03:10:38 EDT 1997

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