<?xml version="1.0" encoding="UTF-8"?>
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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink"
          xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"
          xml:lang="en" xml:id="dtsi">
    <refnamediv>
        <refname>dtsi</refname>
        <refpurpose>Continuous time dynamical systems stable anti-stable decomposition</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            [Ga, Gs, Gi] = dtsi(G)
            [Ga, Gs, Gi] = dtsi(G, tol)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>G</term>
                <listitem>
                    <para>a continuous time linear system.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Ga</term>
                <listitem>
                    <para>a continuous time linear system antistable and strictly proper.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Gs</term>
                <listitem>
                    <para>a continuous time linear system stable and strictly proper.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Gi</term>
                <listitem>
                    <para>real matrix (or polynomial matrix for improper systems)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>
                        optional parameter for detecting stables poles. Default value: <literal>100*%eps</literal>
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            returns the stable-antistable decomposition of <literal>G</literal>:
        </para>
        <para>
            <literal>G= Ga + Gs + Gi</literal>,  <literal>(Gi = G(oo))</literal>
        </para>
        <para>
            <literal>G</literal> can be given in state-space form or in transfer form.
        </para>
        <para>
            <literal>Ga</literal> and <literal>Gs</literal> are returned in the same
            representation (transfer function or state-space) than
            <literal>G</literal>.
        </para>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="syslin">syslin</link>
            </member>
            <member>
                <link linkend="pbig">pbig</link>
            </member>
            <member>
                <link linkend="psmall">psmall</link>
            </member>
            <member>
                <link linkend="pfss">pfss</link>
            </member>
        </simplelist>
    </refsection>

    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
a=0.5;
b=1;
c=2;
sl=syslin('c',a,b,c);
dtsi(sl)
 ]]></programlisting>
    </refsection>
    <refsection>
        <title>History</title>
        <revhistory>
            <revision>
                <revnumber>5.4.0</revnumber>
                <revremark>
                    <literal>Sl</literal> is now checked for continuous time linear dynamical system.
                    This modification has been introduced by this  <ulink url="https://gitlab.com/scilab/scilab/-/commit/3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
                </revremark>
            </revision>
        </revhistory>
    </refsection>
</refentry>
