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1 ## Copyright (C) 1993, 1994, 1995, 2000, 2002, 2004, 2005, 2006, 2007 |
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2 ## Auburn University. All rights reserved. |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} is_stable (@var{a}, @var{tol}, @var{dflg}) |
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22 ## @deftypefnx {Function File} {} is_stable (@var{sys}, @var{tol}) |
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23 ## Returns 1 if the matrix @var{a} or the system @var{sys} |
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24 ## is stable, or 0 if not. |
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25 ## |
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26 ## @strong{Inputs} |
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27 ## @table @var |
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28 ## @item tol |
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29 ## is a roundoff parameter, set to 200*@code{eps} if omitted. |
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30 ## @item dflg |
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31 ## Digital system flag (not required for system data structure): |
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32 ## @table @code |
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33 ## @item @var{dflg} != 0 |
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34 ## stable if eig(a) is in the unit circle |
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35 ## |
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36 ## @item @var{dflg} == 0 |
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37 ## stable if eig(a) is in the open LHP (default) |
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38 ## @end table |
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39 ## @end table |
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40 ## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector |
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41 ## is_observable, is_stabilizable, is_detectable, krylov, krylovb} |
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42 ## @end deftypefn |
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43 |
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44 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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45 ## Created: August 1993 |
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46 ## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for systems |
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47 ## Updated to simpler form by a.s.hodel 1998 |
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48 |
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49 function retval = is_stable (a, tol, disc) |
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50 |
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51 if (nargin < 1 || nargin > 3) |
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52 print_usage (); |
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53 elseif (isstruct (a)) |
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54 ## system was passed |
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55 if (nargin < 3) |
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56 disc = is_digital(a); |
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57 elseif (disc != is_digital (a)) |
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58 warning ("is_stable: disc =%d does not match system", disc) |
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59 endif |
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60 sys = sysupdate (a, "ss"); |
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61 a = sys2ss (sys); |
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62 else |
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63 if (nargin < 3) |
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64 disc = 0; |
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65 endif |
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66 if (issquare (a) == 0) |
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67 error ("A(%dx%d) must be square", rows (A), columns (A)); |
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68 endif |
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69 endif |
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70 |
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71 if (nargin < 2) |
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72 tol = 200*eps; |
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73 elseif (! isscalar (tol)) |
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74 error ("is_stable: tol(%dx%d) must be a scalar", rows (tol), |
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75 columns (tol)); |
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76 endif |
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77 |
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78 l = eig (a); |
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79 if (disc) |
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80 nbad = sum (abs(l)*(1+tol) > 1); |
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81 else |
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82 nbad = sum (real(l)+tol > 0); |
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83 endif |
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84 retval = (nbad == 0); |
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85 |
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86 endfunction |
