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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 |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} obsv (@var{sys}, @var{c}) |
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21 ## @deftypefnx {Function File} {} obsv (@var{a}, @var{c}) |
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22 ## Build observability matrix: |
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23 ## @iftex |
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24 ## @tex |
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25 ## $$ Q_b = \left[ \matrix{ C \cr |
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26 ## CA \cr |
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27 ## CA^2 \cr |
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28 ## \vdots \cr |
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29 ## CA^{n-1} } \right ] $$ |
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30 ## @end tex |
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31 ## @end iftex |
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32 ## @ifinfo |
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33 ## @example |
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34 ## @group |
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35 ## | C | |
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36 ## | CA | |
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37 ## Qb = | CA^2 | |
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38 ## | ... | |
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39 ## | CA^(n-1) | |
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40 ## @end group |
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41 ## @end example |
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42 ## @end ifinfo |
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43 ## of a system data structure or the pair (@var{a}, @var{c}). |
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44 ## |
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45 ## The numerical properties of @command{is_observable} |
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46 ## are much better for observability tests. |
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47 ## @end deftypefn |
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48 |
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49 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> |
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50 ## Created: November 4, 1997 |
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51 |
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52 function Qb = obsv (sys, c) |
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53 |
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54 if (nargin == 2) |
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55 a = sys; |
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56 elseif (nargin == 1 && isstruct(sys)) |
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57 sysupdate(sys,"ss"); |
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58 [a,b,c] = sys2ss(sys); |
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59 else |
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60 print_usage (); |
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61 endif |
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62 |
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63 if (!is_abcd(a,c')) |
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64 Qb = []; |
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65 else |
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66 ## no need to check dimensions, we trust is_abcd(). |
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67 [na, ma] = size(a); |
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68 [nc, mc] = size(c); |
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69 Qb = zeros(na*nc, ma); |
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70 for i = 1:na |
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71 Qb((i-1)*nc+1:i*nc, :) = c; |
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72 c = c * a; |
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73 endfor |
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74 endif |
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75 endfunction |
