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<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
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<LANGUAGE>eng</LANGUAGE>
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<TITLE>inistate</TITLE>
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<TYPE>Scilab Function</TYPE>
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<DATE>April 1999</DATE>
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<SHORT_DESCRIPTION name="inistate"> Estimates the initial state of a discrete-time system</SHORT_DESCRIPTION>
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<CALLING_SEQUENCE_ITEM>X0 = inistate(SYS,Y,U,TOL,PRINTW) </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM>X0 = inistate(A,B,C,Y,U); </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM>X0 = inistate(A,C,Y); </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM> </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM>[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) </CALLING_SEQUENCE_ITEM>
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<PARAM_NAME>SYS</PARAM_NAME>
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<SP>: given system, syslin(dt,A,B,C,D)</SP>
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<PARAM_NAME>Y</PARAM_NAME>
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<SP>: the output of the system</SP>
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<PARAM_NAME>U</PARAM_NAME>
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<SP>: the input of the system</SP>
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<PARAM_NAME>TOL</PARAM_NAME>
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<SP>: TOL is the tolerance used for estimating the rank of matrices. If TOL > 0, then the given value of TOL is used as a lower bound for the reciprocal condition number.</SP>
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Default: prod(size(matrix))*epsilon_machine where epsilon_machine is the relative machine precision.
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<PARAM_NAME>PRINTW</PARAM_NAME>
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<SP>: PRINTW is a switch for printing the warning messages.</SP>
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<PARAM_NAME>= </PARAM_NAME>
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<SP>1: print warning messages;</SP>
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<PARAM_NAME>= </PARAM_NAME>
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<SP>0: do not print warning messages.</SP>
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<PARAM_NAME>X0</PARAM_NAME>
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<SP>: the estimated initial state vector</SP>
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<PARAM_NAME>V</PARAM_NAME>
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<SP>: orthogonal matrix which reduces the system state matrix A to a real Schur form</SP>
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<PARAM_NAME>rcnd</PARAM_NAME>
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<SP>: estimate of the reciprocal condition number of the coefficient matrix of the least squares problem solved.</SP>
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inistate Estimates the initial state of a discrete-time system, given the
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(estimated) system matrices, and a set of input/output data.</P>
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X0 = inistate(SYS,Y,U,TOL,PRINTW) estimates the initial state X0 of
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the discrete-time system SYS = (A,B,C,D), using the output data Y
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and the input data U. The model structure is :</P>
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x(k+1) = Ax(k) + Bu(k), k >= 1,
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The vectors y(k) and u(k) are transposes of the k-th rows of Y and U,
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Instead of the first input parameter SYS (an syslin object), equivalent
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information may be specified using matrix parameters, for instance,
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X0 = inistate(A,B,C,Y,U); or X0 = inistate(A,C,Y);</P>
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[x0,V,rcnd] = inistate(SYS,Y,U,TOL,PRINTW) returns, besides x0,
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the orthogonal matrix V which reduces the system state matrix A to
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a real Schur form, as well as an estimate of the reciprocal condition
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number of the coefficient matrix of the least squares problem solved.</P>
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<LINK>findx0BD</LINK>