Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @lti / lft.m

diff --git a/octave_packages/control-2.3.52/@lti/lft.m b/octave_packages/control-2.3.52/@lti/lft.m
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+## Copyright (C) 2009   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{sys} =} lft (@var{sys1}, @var{sys2})
+## @deftypefnx {Function File} {@var{sys} =} lft (@var{sys1}, @var{sys2}, @var{nu}, @var{ny})
+## Linear fractional tranformation, also known as Redheffer star product.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys1
+## Upper LTI model.
+## @item sys2
+## Lower LTI model.
+## @item nu
+## The last nu inputs of @var{sys1} are connected with the first nu outputs of @var{sys2}.
+## If not specified, @code{min (m1, p2)} is taken.
+## @item ny
+## The last ny outputs of @var{sys1} are connected with the first ny inputs of @var{sys2}.
+## If not specified, @code{min (p1, m2)} is taken.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item sys
+## Resulting LTI model.
+## @end table
+##
+## @strong{Block Diagram}
+## @example
+## @group
+##       .............sys..............
+##       :         +--------+         :
+## w1 ------------>|        |------------> z1
+##       :         |  sys1  |         :
+##       : u +---->|        |-----+ y :
+##       :   |     +--------+     |   :          Lower LFT
+##       :   |                    |   :
+##       :   |     +--------+     |   :          lft (sys1, sys2)
+##       :   +-----|  sys2  |<----+   :
+##       :         +--------+         :
+##       :............................:
+## @end group
+## @end example
+## @example
+## @group
+##       .............sys..............
+##       :         +--------+         :
+##       : u +---->|  sys1  |-----+ y :
+##       :   |     +--------+     |   :          Upper LFT
+##       :   |                    |   :
+##       :   |     +--------+     |   :          lft (sys1, sys2)
+##       :   +-----|        |<----+   :
+##       :         |  sys2  |         :
+## z2 <------------|        |<------------ w2
+##       :         +--------+         :
+##       :............................:
+## @end group
+## @end example
+## @example
+## @group
+##       .............sys..............
+##       :         +--------+         :
+## w1 ------------>|        |------------> z1
+##       :         |  sys1  |         :
+##       : u +---->|        |-----+ y :
+##       :   |     +--------+     |   :
+##       :   |                    |   :          lft (sys1, sys2, nu, ny)
+##       :   |     +--------+     |   :
+##       :   +-----|        |<----+   :
+##       :         |  sys2  |         :
+## z2 <------------|        |<------------ w2
+##       :         +--------+         :
+##       :............................: 
+## @end group
+## @end example
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.2
+
+function sys = lft (sys1, sys2, nu, ny)
+
+  if (nargin != 2 && nargin != 4)
+    print_usage ();
+  endif
+
+  ## object conversion done by sys_group if necessary
+
+  [p1, m1] = size (sys1);
+  [p2, m2] = size (sys2);
+
+  nu_max = min (m1, p2);
+  ny_max = min (m2, p1);
+
+  if (nargin == 2)  # sys = lft (sys1, sys2)
+    nu = nu_max;
+    ny = ny_max;
+  else              # sys = lft (sys1, sys2, nu, ny)
+    if (! is_real_scalar (nu) || nu < 0)
+      error ("lft: argument nu must be a positive integer");
+    endif
+
+    if (! is_real_scalar (ny) || ny < 0)
+      error ("lft: argument ny must be a positive integer");
+    endif
+
+    if (nu > nu_max)
+      error ("lft: argument nu (%d) must be at most %d", nu, nu_max);
+    endif
+
+    if (ny > ny_max)
+      error ("lft: argument ny (%d) must be at most %d", ny, ny_max);
+    endif
+  endif
+
+  M11 = zeros (m1, p1);
+  M12 = [zeros(m1-nu, p2); eye(nu), zeros(nu, p2-nu)];
+  M21 = [zeros(ny, p1-ny), eye(ny); zeros(m2-ny, p1)];
+  M22 = zeros (m2, p2);
+
+  M = [M11, M12; M21, M22];
+
+  in_idx = [1 : (m1-nu), m1 + (ny+1 : m2)];
+  out_idx = [1 : (p1-ny), p1 + (nu+1 : p2)];
+
+  sys = __sys_group__ (sys1, sys2);
+  sys = __sys_connect__ (sys, M);
+  sys = __sys_prune__ (sys, out_idx, in_idx);
+
+  [p, m] = size (sys);
+
+  if (m == 0)
+    warning ("lft: resulting system has no inputs");
+  endif
+
+  if (p == 0)
+    warning ("lft: resulting system has no outputs");
+  endif
+
+endfunction