scilab/modules/cacsd/help/en_US/inistate.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
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  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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="inistate">
  14     <refnamediv>
  15         <refname>inistate</refname>
  16         <refpurpose>Estimates the initial state of a discrete-time system</refpurpose>
  17     </refnamediv>
  18     <refsynopsisdiv>
  19         <title>Calling Sequence</title>
  20         <synopsis>X0 = inistate(SYS,Y,U,TOL,PRINTW)
  21             X0 = inistate(A,B,C,Y,U);
  22             X0 = inistate(A,C,Y);
  23
  24             [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)
  25         </synopsis>
  26     </refsynopsisdiv>
  27     <refsection>
  28         <title>Arguments</title>
  29         <variablelist>
  30             <varlistentry>
  31                 <term>SYS</term>
  32                 <listitem>
  33                     <para>given system, syslin(dt,A,B,C,D)</para>
  34                 </listitem>
  35             </varlistentry>
  36             <varlistentry>
  37                 <term>Y</term>
  38                 <listitem>
  39                     <para>the output of the system</para>
  40                 </listitem>
  41             </varlistentry>
  42             <varlistentry>
  43                 <term>U</term>
  44                 <listitem>
  45                     <para>the input of the system</para>
  46                 </listitem>
  47             </varlistentry>
  48             <varlistentry>
  49                 <term>TOL</term>
  50                 <listitem>
  51                     <para>TOL is the tolerance used for estimating the rank of matrices.  If  TOL &gt; 0,  then the given value of  TOL  is used as a lower bound for the reciprocal condition number.</para>
  52                     <para>
  53                         Default:    prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
  54                     </para>
  55                 </listitem>
  56             </varlistentry>
  57             <varlistentry>
  58                 <term>PRINTW</term>
  59                 <listitem>
  60                     <para>PRINTW is a switch for printing the warning messages.</para>
  61                     <variablelist>
  62                         <varlistentry>
  63                             <term>=  </term>
  64                             <listitem>
  65                                 <para>1: print warning messages;</para>
  66                             </listitem>
  67                         </varlistentry>
  68                         <varlistentry>
  69                             <term>=  </term>
  70                             <listitem>
  71                                 <para>0: do not print warning messages.</para>
  72                             </listitem>
  73                         </varlistentry>
  74                     </variablelist>
  75                     <para>
  76                         Default:    PRINTW = 0.
  77                     </para>
  78                 </listitem>
  79             </varlistentry>
  80             <varlistentry>
  81                 <term>X0</term>
  82                 <listitem>
  83                     <para>the estimated initial state vector</para>
  84                 </listitem>
  85             </varlistentry>
  86             <varlistentry>
  87                 <term>V</term>
  88                 <listitem>
  89                     <para>orthogonal matrix which reduces the system state matrix A to  a real Schur form</para>
  90                 </listitem>
  91             </varlistentry>
  92             <varlistentry>
  93                 <term>rcnd</term>
  94                 <listitem>
  95                     <para>estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</para>
  96                 </listitem>
  97             </varlistentry>
  98         </variablelist>
  99     </refsection>
 100     <refsection>
 101         <title>Description</title>
 102         <para>
 103             inistate  Estimates the initial state of a discrete-time system, given the
 104             (estimated) system matrices, and a set of input/output data.
 105         </para>
 106         <para>
 107             X0 = inistate(SYS,Y,U,TOL,PRINTW)  estimates the initial state X0 of
 108             the discrete-time system SYS = (A,B,C,D), using the output data Y
 109             and the input data U. The model structure is :
 110         </para>
 111         <programlisting role=""><![CDATA[
 112 x(k+1) = Ax(k) + Bu(k),   k >= 1,
 113 y(k)   = Cx(k) + Du(k),
 114  ]]></programlisting>
 115         <para>
 116             The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
 117             respectively.
 118         </para>
 119         <para>
 120             Instead of the first input parameter SYS (an syslin object), equivalent
 121             information may be specified using matrix parameters, for instance,
 122             X0 = inistate(A,B,C,Y,U);   or   X0 = inistate(A,C,Y);
 123         </para>
 124         <para>
 125             [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0,
 126             the orthogonal matrix V which reduces the system state matrix A to
 127             a real Schur form, as well as an estimate of the reciprocal condition
 128             number of the coefficient matrix of the least squares problem solved.
 129         </para>
 130     </refsection>
 131     <refsection role="see also">
 132         <title>See Also</title>
 133         <simplelist type="inline">
 134             <member>
 135                 <link linkend="findBD">findBD</link>
 136             </member>
 137             <member>
 138                 <link linkend="findx0BD">findx0BD</link>
 139             </member>
 140         </simplelist>
 141     </refsection>
 142 </refentry>