extend to RFC3066bis :D
[scilab.git] / scilab / modules / cacsd / help / en_US / inistate.xml
1 <?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
2 <!DOCTYPE MAN SYSTEM "../../../../modules/helptools/help.dtd">
3 <MAN>
4   <LANGUAGE>eng</LANGUAGE>
5   <TITLE>inistate</TITLE>
6   <TYPE>Scilab Function</TYPE>
7   <DATE>$LastChangedDate$</DATE>
8   <SHORT_DESCRIPTION name="inistate"> Estimates the initial state of a discrete-time system</SHORT_DESCRIPTION>
9   <CALLING_SEQUENCE>
10     <CALLING_SEQUENCE_ITEM>X0 = inistate(SYS,Y,U,TOL,PRINTW)   </CALLING_SEQUENCE_ITEM>
11     <CALLING_SEQUENCE_ITEM>X0 = inistate(A,B,C,Y,U);  </CALLING_SEQUENCE_ITEM>
12     <CALLING_SEQUENCE_ITEM>X0 = inistate(A,C,Y);  </CALLING_SEQUENCE_ITEM>
13     <CALLING_SEQUENCE_ITEM>  </CALLING_SEQUENCE_ITEM>
14     <CALLING_SEQUENCE_ITEM>[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW)  </CALLING_SEQUENCE_ITEM>
15   </CALLING_SEQUENCE>
16   <PARAM>
17     <PARAM_INDENT>
18       <PARAM_ITEM>
19         <PARAM_NAME>SYS</PARAM_NAME>
20         <PARAM_DESCRIPTION>
21           <SP>: given system, syslin(dt,A,B,C,D)</SP>
22         </PARAM_DESCRIPTION>
23       </PARAM_ITEM>
24       <PARAM_ITEM>
25         <PARAM_NAME>Y</PARAM_NAME>
26         <PARAM_DESCRIPTION>
27           <SP>: the output of the system</SP>
28         </PARAM_DESCRIPTION>
29       </PARAM_ITEM>
30       <PARAM_ITEM>
31         <PARAM_NAME>U</PARAM_NAME>
32         <PARAM_DESCRIPTION>
33           <SP>: the input of the system</SP>
34         </PARAM_DESCRIPTION>
35       </PARAM_ITEM>
36       <PARAM_ITEM>
37         <PARAM_NAME>TOL</PARAM_NAME>
38         <PARAM_DESCRIPTION>
39           <SP>: 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.</SP>
40           <P>
41     Default:    prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision. 
42   </P>
43         </PARAM_DESCRIPTION>
44       </PARAM_ITEM>
45       <PARAM_ITEM>
46         <PARAM_NAME>PRINTW</PARAM_NAME>
47         <PARAM_DESCRIPTION>
48           <SP>: PRINTW is a switch for printing the warning messages.</SP>
49           <PARAM_INDENT>
50             <PARAM_ITEM>
51               <PARAM_NAME>=  </PARAM_NAME>
52               <PARAM_DESCRIPTION>
53                 <SP>1: print warning messages;</SP>
54               </PARAM_DESCRIPTION>
55             </PARAM_ITEM>
56             <PARAM_ITEM>
57               <PARAM_NAME>=  </PARAM_NAME>
58               <PARAM_DESCRIPTION>
59                 <SP>0: do not print warning messages.</SP>
60               </PARAM_DESCRIPTION>
61             </PARAM_ITEM>
62           </PARAM_INDENT>
63           <P>
64     Default:    PRINTW = 0.
65   </P>
66         </PARAM_DESCRIPTION>
67       </PARAM_ITEM>
68       <PARAM_ITEM>
69         <PARAM_NAME>X0</PARAM_NAME>
70         <PARAM_DESCRIPTION>
71           <SP>: the estimated initial state vector</SP>
72         </PARAM_DESCRIPTION>
73       </PARAM_ITEM>
74       <PARAM_ITEM>
75         <PARAM_NAME>V</PARAM_NAME>
76         <PARAM_DESCRIPTION>
77           <SP>: orthogonal matrix which reduces the system state matrix A to  a real Schur form</SP>
78         </PARAM_DESCRIPTION>
79       </PARAM_ITEM>
80       <PARAM_ITEM>
81         <PARAM_NAME>rcnd</PARAM_NAME>
82         <PARAM_DESCRIPTION>
83           <SP>: estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</SP>
84         </PARAM_DESCRIPTION>
85       </PARAM_ITEM>
86     </PARAM_INDENT>
87   </PARAM>
88   <DESCRIPTION>
89     <P>
90     inistate  Estimates the initial state of a discrete-time system, given the 
91     (estimated) system matrices, and a set of input/output data.</P>
92     <P>
93     X0 = inistate(SYS,Y,U,TOL,PRINTW)  estimates the initial state X0 of 
94     the discrete-time system SYS = (A,B,C,D), using the output data Y
95     and the input data U. The model structure is :</P>
96     <VERBATIM>
97 <![CDATA[
98      x(k+1) = Ax(k) + Bu(k),   k >= 1,
99      y(k)   = Cx(k) + Du(k),
100    ]]>
101     </VERBATIM>
102     <P>
103     The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
104     respectively.</P>
105     <P>
106     Instead of the first input parameter SYS (an syslin object), equivalent
107     information may be specified using matrix parameters, for instance,
108     X0 = inistate(A,B,C,Y,U);   or   X0 = inistate(A,C,Y);</P>
109     <P>
110     [x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0, 
111     the orthogonal matrix V which reduces the system state matrix A to 
112     a real Schur form, as well as an estimate of the reciprocal condition
113     number of the coefficient matrix of the least squares problem solved.</P>
114   </DESCRIPTION>
115   <SEE_ALSO>
116     <SEE_ALSO_ITEM>
117       <LINK>findBD</LINK>
118     </SEE_ALSO_ITEM>
119     <SEE_ALSO_ITEM>
120       <LINK>findx0BD</LINK>
121     </SEE_ALSO_ITEM>
122   </SEE_ALSO>
123 </MAN>