/usr/share/octave/packages/control-3.0.0/lqr.m is in octave-control 3.0.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | ## Copyright (C) 2009-2015 Lukas F. Reichlin
##
## This file is part of LTI Syncope.
##
## LTI Syncope is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## LTI Syncope is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r})
## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r}, @var{s})
## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r})
## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
## Linear-quadratic regulator.
##
## @strong{Inputs}
## @table @var
## @item sys
## Continuous or discrete-time @acronym{LTI} model (p-by-m, n states).
## @item a
## State matrix of continuous-time system (n-by-n).
## @item b
## Input matrix of continuous-time system (n-by-m).
## @item q
## State weighting matrix (n-by-n).
## @item r
## Input weighting matrix (m-by-m).
## @item s
## Optional cross term matrix (n-by-m). If @var{s} is not specified, a zero matrix is assumed.
## @item e
## Optional descriptor matrix (n-by-n). If @var{e} is not specified, an identity matrix is assumed.
## @end table
##
## @strong{Outputs}
## @table @var
## @item g
## State feedback matrix (m-by-n).
## @item x
## Unique stabilizing solution of the continuous-time Riccati equation (n-by-n).
## @item l
## Closed-loop poles (n-by-1).
## @end table
##
## @strong{Equations}
## @example
## @group
## .
## x = A x + B u, x(0) = x0
##
## inf
## J(x0) = INT (x' Q x + u' R u + 2 x' S u) dt
## 0
##
## L = eig (A - B*G)
## @end group
## @end example
## @seealso{care, dare, dlqr}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: November 2009
## Version: 0.2
function [g, x, l] = lqr (a, b, q, r = [], s = [], e = [])
if (nargin < 3 || nargin > 6)
print_usage ();
endif
if (isa (a, "lti"))
s = r;
r = q;
q = b;
[a, b, c, d, e, tsam] = dssdata (a, []);
elseif (nargin < 4)
print_usage ();
else
tsam = 0;
endif
if (issample (tsam, -1))
[x, l, g] = dare (a, b, q, r, s, e);
else
[x, l, g] = care (a, b, q, r, s, e);
endif
endfunction
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