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1 ## Copyright (C) 1996 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 |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} dgram (@var{a}, @var{b}) |
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21 ## Return controllability gramian of discrete time system |
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22 ## @iftex |
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23 ## @tex |
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24 ## $$ x_{k+1} = ax_k + bu_k $$ |
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25 ## @end tex |
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26 ## @end iftex |
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27 ## @ifinfo |
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28 ## @example |
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29 ## x(k+1) = a x(k) + b u(k) |
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30 ## @end example |
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31 ## @end ifinfo |
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32 ## |
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33 ## @strong{Inputs} |
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34 ## @table @var |
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35 ## @item a |
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36 ## @var{n} by @var{n} matrix |
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37 ## @item b |
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38 ## @var{n} by @var{m} matrix |
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39 ## @end table |
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40 ## |
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41 ## @strong{Output} |
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42 ## @table @var |
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43 ## @item m |
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44 ## @var{n} by @var{n} matrix, satisfies |
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45 ## @iftex |
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46 ## @tex |
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47 ## $$ ama^T - m + bb^T = 0 $$ |
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48 ## @end tex |
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49 ## @end iftex |
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50 ## @ifinfo |
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51 ## @example |
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52 ## a m a' - m + b*b' = 0 |
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53 ## @end example |
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54 ## @end ifinfo |
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55 ## @end table |
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56 ## @end deftypefn |
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57 |
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58 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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59 ## Created: July 1995 |
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60 |
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61 function m = dgram (a, b) |
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62 |
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63 ## let dlyap do the error checking... |
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64 |
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65 m = dlyap (a, b*b'); |
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66 |
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67 endfunction |
