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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 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File } {[@var{retval}, @var{U}] =} is_controllable (@var{sys}@{, @var{tol}@}) |
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21 ## @deftypefnx {Function File } {[@var{retval}, @var{U}] =} is_controllable (@var{a}@{, @var{b} ,@var{tol}@}) |
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22 ## Logical check for system controllability. |
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23 ## |
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24 ## @strong{Inputs} |
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25 ## @table @var |
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26 ## @item sys |
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27 ## system data structure |
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28 ## @item a, b |
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29 ## @var{n} by @var{n}, @var{n} by @var{m} matrices, respectively |
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30 ## @item tol |
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31 ## optional roundoff paramter. default value: @code{10*eps} |
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32 ## @end table |
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33 ## |
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34 ## @strong{Outputs} |
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35 ## @table @var |
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36 ## @item retval |
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37 ## Logical flag; returns true (1) if the system @var{sys} or the |
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38 ## pair (@var{a},@var{b}) is controllable, whichever was passed as input arguments. |
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39 ## @item U |
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40 ## U is an orthogonal basis of the controllable subspace. |
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41 ## @end table |
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42 ## |
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43 ## @strong{Method} |
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44 ## Controllability is determined by applying Arnoldi iteration with |
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45 ## complete re-orthogonalization to obtain an orthogonal basis of the |
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46 ## Krylov subspace |
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47 ## @example |
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48 ## span ([b,a*b,...,a^@{n-1@}*b]). |
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49 ## @end example |
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50 ## The Arnoldi iteration is executed with @code{krylov} if the system has a single input; otherwise a block Arnoldi iteration is performed with @code{krylovb}. |
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51 ## |
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52 ## @strong{See also} |
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53 ## @code{is_observable}, @code{is_stabilizable}, @code{is_detectable}, |
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54 ## @code{krylov}, @code{krylovb} |
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55 ## |
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56 ## @end deftypefn |
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57 |
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58 ## See also: size, rows, columns, length, is_matrix, is_scalar, is_vector |
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59 ## is_observable, is_stabilizable, is_detectable, krylov, krylovb |
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60 |
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61 function [retval,U] = is_controllable (a, b, tol) |
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62 |
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63 ## Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993. |
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64 ## Updated by A. S. Hodel (scotte@eng.auburn.edu) Aubust, 1995 to use krylovb |
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65 ## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for packed systems |
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66 |
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67 deftol = 1; # assume default tolerance |
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68 if(nargin < 1 | nargin > 3) |
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69 usage("[retval,U] = %s\n\t%s", "is_controllable(a {, b ,tol})", ... |
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70 "is_controllable(sys{,tol})"); |
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71 elseif(is_struct(a)) |
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72 ## system structure passed. |
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73 sys = sysupdate(a,"ss"); |
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74 [a,bs] = sys2ss(sys); |
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75 if(nargin > 2) |
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76 usage("[retval,U] = is_controllable(sys{,tol})"); |
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77 elseif(nargin == 2) |
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78 tol = b; % get tolerance |
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79 deftol = 0; |
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80 endif |
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81 b = bs; |
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82 else |
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83 ## a,b arguments sent directly. |
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84 if(nargin < 2) |
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85 usage("[retval,U] = is_controllable(a {, b ,tol})"); |
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86 else |
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87 deftol = 1; |
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88 endif |
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89 endif |
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90 |
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91 ## check for default tolerance |
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92 if(deftol) tol = 1000*eps; endif |
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93 |
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94 ## check tol dimensions |
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95 if( !is_scalar(tol) ) |
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96 error("is_controllable: tol(%dx%d) must be a scalar", ... |
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97 rows(tol),columns(tol)); |
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98 elseif( !is_sample(tol) ) |
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99 error("is_controllable: tol=%e must be positive",tol); |
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100 endif |
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101 |
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102 ## check dimensions compatibility |
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103 n = is_square (a); |
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104 [nr, nc] = size (b); |
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105 |
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106 if (n == 0 | n != nr | nc == 0) |
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107 warning("is_controllable: a=(%dx%d), b(%dx%d)",rows(a),columns(a),nr,nc); |
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108 retval = 0; |
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109 else |
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110 ## call block-krylov subspace routine to get an orthogonal basis |
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111 ## of the controllable subspace. |
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112 [U,H,Ucols] = krylov(a,b,n,tol,1); |
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113 retval = (Ucols == n); |
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114 endif |
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115 endfunction |
