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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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<TYPE>Scilab Function</TYPE>
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<DATE>April 1993</DATE>
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<SHORT_DESCRIPTION name="arsimul"> armax simulation</SHORT_DESCRIPTION>
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<CALLING_SEQUENCE_ITEM>[z]=arsimul(a,b,d,sig,u,[up,yp,ep]) </CALLING_SEQUENCE_ITEM>
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<CALLING_SEQUENCE_ITEM>[z]=arsimul(ar,u,[up,yp,ep]) </CALLING_SEQUENCE_ITEM>
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<PARAM_NAME>ar</PARAM_NAME>
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<SP>: an armax process. See armac.</SP>
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<PARAM_NAME>a</PARAM_NAME>
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<SP>: is the matrix[Id,a1,...,a_r] of dimension (n,(r+1)*n)</SP>
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<PARAM_NAME>b</PARAM_NAME>
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<SP>: is the matrix[b0,......,b_s] of dimension (n,(s+1)*m)</SP>
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<PARAM_NAME>d</PARAM_NAME>
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<SP>: is the matrix[Id,d_1,......,d_t] of dimension (n,(t+1)*n)</SP>
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<PARAM_NAME>u</PARAM_NAME>
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<SP>: is a matrix (m,N), which gives the entry u(:,j)=u_j</SP>
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<PARAM_NAME>sig</PARAM_NAME>
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<SP>: is a (n,n) matrix e_{k} is an n-dimensional Gaussian process with variance I</SP>
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<PARAM_NAME>up, yp</PARAM_NAME>
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<SP>: optional parameter which describe the past. up=[ u_0,u_{-1},...,u_{s-1}]; yp=[ y_0,y_{-1},...,y_{r-1}]; ep=[ e_0,e_{-1},...,e_{r-1}]; if they are omitted, the past value are supposed to be zero</SP>
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<PARAM_NAME>z</PARAM_NAME>
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<SP>: z=[ y(1),....,y(N)]</SP>
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simulation of an n-dimensional armax process
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A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)</P>
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A(z)= Id+a1*z+...+a_r*z^r; ( r=0 => A(z)=Id)
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B(z)= b0+b1*z+...+b_s z^s; ( s=-1 => B(z)=[])
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D(z)= Id+d1*z+...+d_t z^t; ( t=0 => D(z)=Id)
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z et e are in R^n et u in R^m</P>
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<SECTION label="Method">
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a state-space representation is constructed and ode with the option "discr" is used to compute z</P>
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<AUTHOR>J-Ph.C.; </AUTHOR>