← Back to branch summary

~ubuntu-branches/ubuntu/raring/scilab/raring-proposed

« back to all changes in this revision

Viewing changes to modules/cacsd/help/en_US/gcare.xml

  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

Show diffs side-by-side

added added

removed removed

Lines of Context:
modules/cacsd/help/en_US/gcare.xml
11
11
 *
12
12
 -->
13
13
<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" version="5.0-subset Scilab" xml:lang="en" xml:id="gcare">
14
 
  <refnamediv>
15
 
    <refname>gcare</refname>
16
 
    <refpurpose>Continuous time control Riccati equation</refpurpose>
17
 
  </refnamediv>
18
 
  <refsynopsisdiv>
19
 
    <title>Calling Sequence</title>
20
 
    <synopsis>[X,F]=gcare(Sl)</synopsis>
21
 
  </refsynopsisdiv>
22
 
  <refsection>
23
 
    <title>Arguments</title>
24
 
    <variablelist>
25
 
      <varlistentry>
26
 
        <term>Sl</term>
27
 
        <listitem>
28
 
          <para>a continuous time linear dynamical system in state-space representation</para>
29
 
        </listitem>
30
 
      </varlistentry>
31
 
      <varlistentry>
32
 
        <term>X</term>
33
 
        <listitem>
34
 
          <para>symmetric matrix</para>
35
 
        </listitem>
36
 
      </varlistentry>
37
 
      <varlistentry>
38
 
        <term>F</term>
39
 
        <listitem>
40
 
          <para>real matrix</para>
41
 
        </listitem>
42
 
      </varlistentry>
43
 
    </variablelist>
44
 
  </refsection>
45
 
  <refsection>
46
 
    <title>Description</title>
47
 
    <para>
48
 
      Generalized Control Algebraic Riccati Equation (GCARE).
49
 
      <literal>X</literal> = solution , <literal>F</literal> = gain.
50
 
    </para>
51
 
    <para>
52
 
      The GCARE for <literal>Sl=[A,B,C,D]</literal> is:
53
 
    </para>
54
 
    <programlisting role=""><![CDATA[ 
 
14
    <refnamediv>
 
15
        <refname>gcare</refname>
 
16
        <refpurpose>Continuous time control Riccati equation</refpurpose>
 
17
    </refnamediv>
 
18
    <refsynopsisdiv>
 
19
        <title>Calling Sequence</title>
 
20
        <synopsis>[X,F]=gcare(Sl)</synopsis>
 
21
    </refsynopsisdiv>
 
22
    <refsection>
 
23
        <title>Arguments</title>
 
24
        <variablelist>
 
25
            <varlistentry>
 
26
                <term>Sl</term>
 
27
                <listitem>
 
28
                    <para>a continuous time linear dynamical system in state-space representation</para>
 
29
                </listitem>
 
30
            </varlistentry>
 
31
            <varlistentry>
 
32
                <term>X</term>
 
33
                <listitem>
 
34
                    <para>symmetric matrix</para>
 
35
                </listitem>
 
36
            </varlistentry>
 
37
            <varlistentry>
 
38
                <term>F</term>
 
39
                <listitem>
 
40
                    <para>real matrix</para>
 
41
                </listitem>
 
42
            </varlistentry>
 
43
        </variablelist>
 
44
    </refsection>
 
45
    <refsection>
 
46
        <title>Description</title>
 
47
        <para>
 
48
            Generalized Control Algebraic Riccati Equation (GCARE).
 
49
            <literal>X</literal> = solution , <literal>F</literal> = gain.
 
50
        </para>
 
51
        <para>
 
52
            The GCARE for <literal>Sl=[A,B,C,D]</literal> is:
 
53
        </para>
 
54
        <programlisting role=""><![CDATA[ 
55
55
(A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
56
56
 ]]></programlisting>
57
 
    <para>
58
 
      where <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal> 
59
 
      and <literal>F=-Si*(D'*C+B'*X)</literal> is such that <literal>A+B*F</literal> is stable.
60
 
    </para>
61
 
  </refsection>
62
 
  <refsection role="see also">
63
 
    <title>See Also</title>
64
 
    <simplelist type="inline">
65
 
      <member>
66
 
        <link linkend="gfare">gfare</link>
67
 
      </member>
68
 
    </simplelist>
69
 
  </refsection>
70
 
  <refsection>
71
 
    <title>History</title>
72
 
    <revhistory>
73
 
      <revision>
74
 
        <revnumber>5.4.0</revnumber>
75
 
        <revremark>
76
 
          <literal>Sl</literal> is now checked for
77
 
          continuous time linear dynamical system.  This modification
78
 
          has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
79
 
        </revremark>
80
 
      </revision>
81
 
    </revhistory>
82
 
  </refsection>
 
57
        <para>
 
58
            where <literal>S=(eye()+D'*D)</literal>, <literal>Si=inv(S)</literal>, <literal>R=(eye()+D*D')</literal>, <literal>Ri=inv(R)</literal> 
 
59
            and <literal>F=-Si*(D'*C+B'*X)</literal> is such that <literal>A+B*F</literal> is stable.
 
60
        </para>
 
61
    </refsection>
 
62
    <refsection role="see also">
 
63
        <title>See Also</title>
 
64
        <simplelist type="inline">
 
65
            <member>
 
66
                <link linkend="gfare">gfare</link>
 
67
            </member>
 
68
        </simplelist>
 
69
    </refsection>
 
70
    <refsection>
 
71
        <title>History</title>
 
72
        <revhistory>
 
73
            <revision>
 
74
                <revnumber>5.4.0</revnumber>
 
75
                <revremark>
 
76
                    <literal>Sl</literal> is now checked for
 
77
                    continuous time linear dynamical system.  This modification
 
78
                    has been introduced by this <ulink url="http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d">commit</ulink>
 
79
                </revremark>
 
80
            </revision>
 
81
        </revhistory>
 
82
    </refsection>
83
83
</refentry>