The function computes the coprime factors of the stabilizable and detectable state space realization
.
For each proper real rational transfer matrix , there exist eight transfer matrices in
satisfying the equations:
![Rendered by QuickLaTeX.com (N,M)](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-faa93565bfa26481100d1a86f6bc6207_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com (\tilde{N},\tilde{M})](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-af5302f6d709b50855d57ddc54847a89_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com G](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-30a79c32f18567063fe44716929e7ced_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com \left(\begin{array}{c}M\\N\end{array}\right)](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-2a3a45b8e0e499369a6d31fe93655200_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com \left(\begin{array}{cc}\tilde{N}&\tilde{M}\end{array}\right)](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-74c023a28376312547d890b73bd13f5d_l3.png?media=1702023987)
Let be a stabilizable and detectable realization and choose
,
, and
as:
![Rendered by QuickLaTeX.com P](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com Z](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png?media=1702023987)
Define the state feedback and observer gains and
as:
![Rendered by QuickLaTeX.com (N,M)](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-faa93565bfa26481100d1a86f6bc6207_l3.png?media=1702023987)
![Rendered by QuickLaTeX.com (\tilde{N},\tilde{M})](https://usercontent.one/wp/www.iqclab.eu/wp-content/ql-cache/quicklatex.com-af5302f6d709b50855d57ddc54847a89_l3.png?media=1702023987)
As output the function provides the structures and
with the realizations of respectively:
,
,
,
,
,
,
,
,