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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="sensi">
    <refnamediv>
        <refname>sensi</refname>
        <refpurpose>sensitivity functions</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>
            [Se, Re, Te] = sensi(G, K)
            [Si, Ri, Ti] = sensi(G, K, flag)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>G</term>
                <listitem>
                    <para>
                        standard plant (<literal>syslin</literal> list)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>K</term>
                <listitem>
                    <para>
                        compensator (<literal>syslin</literal> list)
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>flag</term>
                <listitem>
                    <para>
                        character string <literal>'o'</literal> (default value) or <literal>'i'</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Se</term>
                <listitem>
                    <para>
                        output sensitivity function <literal>(I+G*K)^-1</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Re</term>
                <listitem>
                    <para>
                        <literal>K*Se</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Te</term>
                <listitem>
                    <para>
                        <literal>G*K*Se</literal> (output complementary sensitivity function)
                    </para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>sensi</literal> computes sensitivity functions. If <literal>G</literal> and <literal>K</literal> are
            given in state-space form, the systems returned are generically minimal.
            Calculation is made by <literal>lft</literal>, e.g.,
            <literal>Se</literal> can be given by the commands
            <literal> P = augment(G,'S')</literal>, <literal>Se=lft(P,K)</literal>.
            If <literal>flag</literal> = <literal>'i'</literal>, <literal>[Si,Ri,Ti]=sensi(G,K,'i')</literal>
            returns the input sensitivity functions.
        </para>
        <programlisting role=""><![CDATA[
[Se;Re;Te]= [inv(eye()+G*K);K*inv(eye()+G*K);G*K*inv(eye()+G*K)];
[Si;Ri;Ti]= [inv(eye()+K*G);G*inv(eye()+K*G);K*G*inv(eye()+K*G)];
 ]]></programlisting>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
G=ssrand(1,1,3);
K=ssrand(1,1,3);
[Se,Re,Te]=sensi(G,K);
Se1=inv(eye()+G*K);  //Other way to compute
ss2tf(Se)    //Se seen in transfer form
ss2tf(Se1)
ss2tf(Te)
ss2tf(G*K*Se1)
[Si,Ri,Ti]=sensi(G,K,'i');
w1=[ss2tf(Si);ss2tf(Ri);ss2tf(Ti)]
w2=[ss2tf(inv(eye()+K*G));ss2tf(G*inv(eye()+K*G));ss2tf(K*G*inv(eye()+K*G))];
clean(w1-w2)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="augment">augment</link>
            </member>
            <member>
                <link linkend="lft">lft</link>
            </member>
            <member>
                <link linkend="h_cl">h_cl</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
