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D.10.2.2 controlDim

Procedure from library control.lib (see control_lib).

Usage:
controlDim(R); R a module (R is the matrix of the system of equations to be investigated)

Return:
list

Purpose:
computes list of all the properties concerning controllability of the system (behavior), represented by the matrix R

Note:
this procedure is analogous to 'control' but uses dimension calculations.This approach works for full row rank matrices only.

Example:
 
LIB "control.lib";
//a WindTunnel example
ring A = (0,a, omega, zeta, k),(D1, delta),dp;
module R;
R = [D1+a, -k*a*delta, 0, 0],
[0, D1, -1, 0],
[0, omega^2, D1+2*zeta*omega, -omega^2];
R=transpose(R);
view(R);
==> D1+(a),(-a*k)*delta,0                ,0         ,
==> 0     ,D1          ,-1               ,0         ,
==> 0     ,(omega^2)   ,D1+(2*omega*zeta),(-omega^2)
view(controlDim(R));
==> number of first nonzero Ext:
==> 
==> 2
==> 
==> controllable, not reflexive, image representation:
==> 
==> (a*omega^2*k)*delta                                               ,
==> (omega^2)*D1+(a*omega^2)                                          ,
==> (omega^2)*D1^2+(a*omega^2)*D1                                     ,
==> D1^3+(a+2*omega*zeta)*D1^2+(2*a*omega*zeta+omega^2)*D1+(a*omega^2)
==> 
==> dimension of the system:
==> 
==> 2
==> 
==> Parameter constellations which might lead to a non-controllable system:
==> 
==> a,k,omega
==> 
==> 


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