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1 ## Copyright (C) 1996, 1998, 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} {} h2norm (@var{sys}) |
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22 ## Computes the |
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23 ## @iftex |
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24 ## @tex |
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25 ## $ { \cal H }_2 $ |
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26 ## @end tex |
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27 ## @end iftex |
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28 ## @ifinfo |
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29 ## H-2 |
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30 ## @end ifinfo |
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31 ## norm of a system data structure (continuous time only). |
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32 ## |
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33 ## Reference: |
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34 ## Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions to Standard} |
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35 ## @iftex |
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36 ## @tex |
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37 ## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $ |
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38 ## @end tex |
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39 ## @end iftex |
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40 ## @ifinfo |
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41 ## @cite{H-2 and H-infinity} |
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42 ## @end ifinfo |
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43 ## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989. |
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44 ## @end deftypefn |
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45 |
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46 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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47 ## Created: August 1995 |
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48 ## updated for system data structure by John Ingram November 1996 |
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49 |
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50 function h2gain = h2norm (sys) |
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51 |
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52 if (nargin != 1) |
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53 print_usage (); |
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54 elseif (! isstruct (sys)) |
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55 error ("Sys must be in system data structure"); |
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56 endif |
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57 dflg = is_digital (sys); |
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58 |
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59 if (! is_stable (sys)) |
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60 warning ("h2norm: unstable input system; returning Inf"); |
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61 h2gain = Inf; |
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62 else |
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63 ## compute gain |
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64 [a, b, c, d] = sys2ss (sys); |
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65 if (dflg) |
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66 M = dlyap (a, b*b'); |
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67 else |
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68 M = lyap (a, b*b'); |
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69 endif |
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70 if (min (real (eig (M))) < 0) |
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71 error ("h2norm: gramian not >= 0 (lightly damped modes?)") |
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72 endif |
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73 |
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74 h2gain = sqrt (trace (d*d' + c*M*c')); |
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75 endif |
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76 |
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77 endfunction |
