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1 # Copyright (C) 1993, 1994, 1995 Auburn University. All Rights Reserved |
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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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 |
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19 function [retval,U] = is_controllable (a, b, tol) |
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20 # [retval, U] = is_controllable (a, b {,tol}) |
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21 # = is_controllable (sys{, tol}) |
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22 # Returns retval=1 if the system sys or the pair (a, b) is controllable |
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23 # 0 if not. |
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24 # U is an orthogonal basis of the controllable subspace. |
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25 # |
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26 # Controllability is determined by applying Arnoldi iteration with |
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27 # complete re-orthogonalization to obtain an orthogonal basis of the |
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28 # Krylov subspace. |
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29 # |
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30 # span ([b,a*b,...,a^ b]). |
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31 # |
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32 # tol is a roundoff paramter, set to 10*eps if omitted. |
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33 # |
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34 # See also: size, rows, columns, length, is_matrix, is_scalar, is_vector |
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35 # is_observable, is_stabilizable, is_detectable, krylov, krylovb |
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36 |
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37 # Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993. |
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38 # Updated by A. S. Hodel (scotte@eng.auburn.edu) Aubust, 1995 to use krylovb |
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39 # Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for packed systems |
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40 |
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41 deftol = 1; # assume default tolerance |
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42 if(nargin < 1 | nargin > 3) |
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43 usage("[retval,U] = %s\n\t%s", "is_controllable(a {, b ,tol})", ... |
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44 "is_controllable(sys{,tol})"); |
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45 elseif(is_struct(a)) |
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46 # system structure passed. |
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47 sys = sysupdate(a,"ss"); |
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48 [a,bs] = sys2ss(sys); |
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49 if(nargin > 2) |
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50 usage("[retval,U] = is_controllable(sys{,tol})"); |
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51 elseif(nargin == 2) |
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52 tol = b; % get tolerance |
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53 deftol = 0; |
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54 endif |
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55 b = bs; |
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56 else |
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57 # a,b arguments sent directly. |
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58 if(nargin < 2) |
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59 usage("[retval,U] = is_controllable(a {, b ,tol})"); |
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60 else |
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61 deftol = 1; |
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62 endif |
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63 endif |
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64 |
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65 # check for default tolerance |
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66 if(deftol) tol = 1000*eps; endif |
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67 |
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68 # check tol dimensions |
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69 if( !is_scalar(tol) ) |
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70 error("is_controllable: tol(%dx%d) must be a scalar", ... |
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71 rows(tol),columns(tol)); |
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72 elseif( !is_sample(tol) ) |
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73 error("is_controllable: tol=%e must be positive",tol); |
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74 endif |
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75 |
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76 # check dimensions compatibility |
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77 n = is_square (a); |
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78 [nr, nc] = size (b); |
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79 |
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80 if (n == 0 | n != nr | nc == 0) |
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81 warning("is_controllable: a=(%dx%d), b(%dx%d)",rows(a),columns(a),nr,nc); |
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82 retval = 0; |
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83 else |
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84 # call block-krylov subspace routine to get an orthogonal basis |
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85 # of the controllable subspace. |
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86 [U,H,Ucols] = krylov(a,b,n,tol,1); |
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87 retval = (Ucols == n); |
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88 endif |
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89 endfunction |
