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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from sos2ss.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="sos2ss" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns3="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>sos2ss</refname>
<refpurpose>Converts Digital Filter Second order section parameters to steady state form. </refpurpose>
</refnamediv>
<refsection>
<title>Calling Sequence</title>
[A,B,C,D] = sos2ss(sos)
[A,B,C,D] = sos2ss(sos,g)
</refsection>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>[A,B,C,D]:</term>
<listitem><para>Steady state parameters.</para></listitem></varlistentry>
<varlistentry><term>sos:</term>
<listitem><para> Second order sectional matrix.</para></listitem></varlistentry>
<varlistentry><term>g:</term>
<listitem><para>gain of the system.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>sos2ss converts a second-order section representation of a digital filter to an equivalent state-space representation.</para>
<para>
[A,B,C,D] = sos2ss(sos) converts sos, a system expressed in second-order section form, to a single-input, single-output state-space representation:
x(n+1)=Ax(n)+Bu(n),
y(n)=Cx(n)+Du(n).</para>
<para>
<latex>
\begin{eqnarray}
f(x,a,r) = \frac{1}{r^{-a}\Gamma(a)} \int_0^x t^{a-1} \exp\left(-rt\right) dt
\end{eqnarray}
</latex>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
sos = [1 1 1 1 0 -1 ;
-2 3 1 1 10 1];
[A,B,C,D] = sos2ss(sos,2);
//EXPECTED OUTPUT:
//D =- 4.
//C =42. 4. - 32. - 2.
//B =[1. 0. 0. 0. 0.]'
//A =[- 10. 0. 10. 1. ; 1. 0. 0. 0. ; 0. 1. 0. 0. ; 0. 0. 1. 0. ]
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Parthasrathi Panda</member>
</simplelist>
</refsection>
<refsection>
<title>See also</title>
<simplelist type="inline">
<member><link linkend="sos2tf">abs</link></member>
<member><link linkend="sosbreak">mean</link></member>
<member><link linkend="sos2ss">max</link></member>
</simplelist>
</refsection>
</refentry>
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