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1 ## Copyright (C) 1997 Kai P. Mueller |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by the |
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7 ## Free Software Foundation; either version 2, or (at your option) any |
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8 ## later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 ## for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} ctrb (@var{sys}, @var{b}) |
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22 ## @deftypefnx {Function File} {} ctrb (@var{a}, @var{b}) |
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23 ## Build controllability matrix: |
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24 ## @iftex |
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25 ## @tex |
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26 ## $$ Q_s = [ B AB A^2B \ldots A^{n-1}B ] $$ |
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27 ## @end tex |
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28 ## @end iftex |
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29 ## @ifinfo |
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30 ## @example |
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31 ## 2 n-1 |
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32 ## Qs = [ B AB A B ... A B ] |
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33 ## @end example |
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34 ## @end ifinfo |
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35 ## |
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36 ## of a system data structure or the pair (@var{a}, @var{b}). |
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37 ## |
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38 ## @command{ctrb} forms the controllability matrix. |
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39 ## The numerical properties of @command{is_controllable} |
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40 ## are much better for controllability tests. |
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41 ## @end deftypefn |
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42 |
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43 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> |
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44 ## Created: November 4, 1997 |
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45 ## based on is_controllable.m of Scottedward Hodel |
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46 |
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47 function Qs = ctrb (sys, b) |
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48 |
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49 if (nargin == 2) |
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50 a = sys; |
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51 elseif (nargin == 1 && isstruct(sys)) |
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52 sysupdate(sys,"ss"); |
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53 [a,b] = sys2ss(sys); |
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54 else |
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55 print_usage (); |
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56 endif |
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57 |
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58 if (!is_abcd(a,b)) |
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59 Qs = []; |
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60 else |
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61 ## no need to check dimensions, we trust is_abcd(). |
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62 [na, ma] = size(a); |
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63 ## using imb avoids name conflict with the "mb" function |
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64 [inb, imb] = size(b); |
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65 Qs = zeros(na, ma*imb); |
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66 for i = 1:na |
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67 Qs(:, (i-1)*imb+1:i*imb) = b; |
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68 b = a * b; |
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69 endfor |
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70 endif |
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71 endfunction |
