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1 ## Copyright (C) 1996, 1998 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} {} 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 usage("h2gain = h2norm(sys)"); |
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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 end |
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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 endfunction |
