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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="linfn">
    <refnamediv>
        <refname>linfn</refname>
        <refpurpose>infinity norm</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[x, freq] = linfn(G, PREC, RELTOL, options)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>G</term>
                <listitem>
                    <para>
                        is a <literal>syslin</literal> list
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>PREC</term>
                <listitem>
                    <para>desired relative accuracy on the norm</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>RELTOL</term>
                <listitem>
                    <para>relative threshold to decide when an eigenvalue can be  considered on the imaginary axis.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>options</term>
                <listitem>
                    <para>
                        available options are <literal>'trace'</literal> or <literal>'cond'</literal>
                    </para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>x</term>
                <listitem>
                    <para>is the computed norm.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>freq</term>
                <listitem>
                    <para>vector</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Computes the Linf (or Hinf) norm of <literal>G</literal>
            This norm is well-defined as soon as the realization
            <literal>G=(A,B,C,D)</literal> has no imaginary eigenvalue which is both
            controllable and observable.
        </para>
        <para>
            <literal>freq</literal> is a list of the frequencies for which <literal>||G||</literal> is
            attained,i.e., such that <literal>||G (j om)|| = ||G||</literal>.
        </para>
        <para>
            If -1 is in the list, the norm is attained at infinity.
        </para>
        <para>
            If -2 is in the list, <literal>G</literal> is all-pass in some direction so that
            <literal>||G (j omega)|| = ||G||</literal> for all frequencies omega.
        </para>
        <para>
            The algorithm follows the paper by G. Robel
            (AC-34 pp. 882-884, 1989).
            The case <literal>D=0</literal> is not treated separately due to superior
            accuracy of the general method when <literal>(A,B,C)</literal> is nearly
            non minimal.
        </para>
        <para>
            The <literal>'trace'</literal> option traces each bisection step, i.e., displays
            the lower and upper bounds and the current test point.
        </para>
        <para>
            The <literal>'cond'</literal> option estimates a confidence index on the computed
            value and issues a warning if computations are
            ill-conditioned
        </para>
        <para>
            In the general case (<literal>A</literal> neither stable nor anti-stable),
            no upper bound is  prespecified.
        </para>
        <para>
            If by contrast <literal>A</literal> is stable or anti stable, lower
            and upper bounds are computed using the associated
            Lyapunov solutions.
        </para>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="h_norm">h_norm</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
