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1 ### Copyright (C) 1996 John W. Eaton |
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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 2, or (at your option) |
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8 ### 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, write to the Free |
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17 ### Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ### 02111-1307, USA. |
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19 |
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20 function retval = is_controllable (a, b, tol) |
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21 |
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22 ## Usage: is_controllable (a, b {,tol}) |
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23 ## |
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24 ## Returns 1 if the pair (a, b) is controllable, or 0 if not. |
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25 ## |
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26 ## See also: size, rows, columns, length, is_matrix, is_scalar, is_vector |
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27 ## |
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28 ## This should really use the method below, but I'm being lazy for now: |
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29 ## |
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30 ## Controllability is determined by applying Arnoldi iteration with |
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31 ## complete re-orthogonalization to obtain an orthogonal basis of the |
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32 ## Krylov subspace. |
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33 ## |
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34 ## (FIX ME... The Krylov subspace approach is not done yet!) |
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35 ## n-1 |
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36 ## span ([b,a*b,...,a^ b]). |
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37 ## |
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38 ## tol is a roundoff paramter, set to 2*eps if omitted. |
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39 |
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40 ## Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993. |
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41 |
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42 if (nargin == 2 || nargin == 3) |
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43 |
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44 n = is_square (a); |
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45 [nr, nc] = size (b); |
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46 |
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47 if (n == 0 || n != nr || nc == 0) |
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48 retval = 0; |
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49 else |
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50 |
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51 m = b; |
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52 tmp = b; |
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56
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53 for ii = 1:(n-1) |
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54 tmp = a * tmp; |
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55 m = [m, tmp]; |
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56 endfor |
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57 |
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58 ## If n is of any significant size, m will be low rank, so be careful! |
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59 |
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60 if (nargin == 3) |
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61 if (is_scalar (tol)) |
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62 retval = (rank (m, tol) == n); |
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63 else |
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64 error ("is_controllable: tol must be a scalar"); |
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65 endif |
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66 else |
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67 retval = (rank (m) == n); |
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68 endif |
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69 endif |
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70 else |
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71 usage ("is_controllable (a, b)"); |
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72 endif |
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73 |
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74 endfunction |
