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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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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 ## @end deftypefn |
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41 ## |
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42 ## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector |
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43 ## is_observable, is_stabilizable, is_detectable, krylov, and krylovb} |
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44 |
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45 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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46 ## Created: August 1993 |
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47 ## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for systems |
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48 ## Updated to simpler form by a.s.hodel 1998 |
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49 |
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50 function retval = is_stable (a, tol, disc) |
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51 |
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52 if( (nargin < 1) | (nargin > 3) ) usage("is_stable(a {,tol,disc})"); |
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53 elseif(isstruct(a)) |
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54 ## system was passed |
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55 if(nargin < 3) disc = is_digital(a); |
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56 elseif(disc != is_digital(a)) |
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57 warning("is_stable: disc =%d does not match system",disc) |
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58 endif |
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59 sys = sysupdate(a,"ss"); |
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60 a = sys2ss(sys); |
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61 else |
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62 if(nargin < 3) disc = 0; endif |
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63 if(issquare(a) == 0) |
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64 error("A(%dx%d) must be square",rows(A), columns(A)); |
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65 endif |
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66 endif |
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67 |
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68 if(nargin < 2) tol = 200*eps; |
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69 elseif( !isscalar(tol) ) |
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70 error("is_stable: tol(%dx%d) must be a scalar",rows(tol),columns(tol)); |
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71 endif |
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72 |
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73 l = eig(a); |
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74 if(disc) nbad = sum(abs(l)*(1+tol) > 1); |
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75 else nbad = sum(real(l)+tol > 0); endif |
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76 retval = (nbad == 0); |
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77 |
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78 endfunction |
