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+## Copyright (C) 2009, 2010   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{P} =} augw (@var{G}, @var{W1}, @var{W2}, @var{W3})
+## Extend plant for stacked S/KS/T problem.  Subsequently, the robust control problem
+## can be solved by h2syn or hinfsyn.
+##
+## @strong{Inputs}
+## @table @var
+## @item G
+## LTI model of plant.
+## @item W1
+## LTI model of performance weight.  Bounds the largest singular values of sensitivity @var{S}.
+## Model must be empty @code{[]}, SISO or of appropriate size.
+## @item W2
+## LTI model to penalize large control inputs.  Bounds the largest singular values of @var{KS}.
+## Model must be empty @code{[]}, SISO or of appropriate size.
+## @item W3
+## LTI model of robustness and noise sensitivity weight.  Bounds the largest singular values of 
+## complementary sensitivity @var{T}.  Model must be empty @code{[]}, SISO or of appropriate size.
+## @end table
+##
+## All inputs must be proper/realizable.
+## Scalars, vectors and matrices are possible instead of LTI models.
+##
+## @strong{Outputs}
+## @table @var
+## @item P
+## State-space model of augmented plant.
+## @end table
+##
+## @strong{Block Diagram}
+## @example
+## @group
+##
+##     | W1 | -W1*G |     z1 = W1 r  -  W1 G u
+##     | 0  |  W2   |     z2 =          W2   u
+## P = | 0  |  W3*G |     z3 =          W3 G u
+##     |----+-------|
+##     | I  |    -G |     e  =    r  -     G u
+## @end group
+## @end example
+## @example
+## @group
+##                                                       +------+  z1
+##             +---------------------------------------->|  W1  |----->
+##             |                                         +------+
+##             |                                         +------+  z2
+##             |                 +---------------------->|  W2  |----->
+##             |                 |                       +------+
+##  r   +    e |   +--------+  u |   +--------+  y       +------+  z3
+## ----->(+)---+-->|  K(s)  |----+-->|  G(s)  |----+---->|  W3  |----->
+##        ^ -      +--------+        +--------+    |     +------+
+##        |                                        |
+##        +----------------------------------------+
+## @end group
+## @end example
+## @example
+## @group
+##                +--------+
+##                |        |-----> z1 (p1x1)          z1 = W1 e
+##  r (px1) ----->|  P(s)  |-----> z2 (p2x1)          z2 = W2 u
+##                |        |-----> z3 (p3x1)          z3 = W3 y
+##  u (mx1) ----->|        |-----> e (px1)            e = r - y
+##                +--------+
+## @end group
+## @end example
+## @example
+## @group
+##                +--------+  
+##        r ----->|        |-----> z
+##                |  P(s)  |
+##        u +---->|        |-----+ e
+##          |     +--------+     |
+##          |                    |
+##          |     +--------+     |
+##          +-----|  K(s)  |<----+
+##                +--------+
+## @end group
+## @end example
+## @example
+## @group
+## Reference:
+## Skogestad, S. and Postlethwaite I.
+## Multivariable Feedback Control: Analysis and Design
+## Second Edition
+## Wiley 2005
+## Chapter 3.8: General Control Problem Formulation
+## @end group
+## @end example
+## @seealso{h2syn, hinfsyn, mixsyn}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: December 2009
+## Version: 0.2
+
+function P = augw (G, W1 = [], W2 = [], W3 = [])
+
+  if (nargin == 0 || nargin > 4)
+    print_usage ();
+  endif
+
+  G = ss (G);
+  [p, m] = size (G);
+
+  [W1, p1, m1] = __adjust_weighting__ (W1, p);
+  [W2, p2, m2] = __adjust_weighting__ (W2, m);
+  [W3, p3, m3] = __adjust_weighting__ (W3, p);
+
+  ## Pr = [1; 0; 0; 1];
+  ## Pu = [-1; 0; 1; -1]*G + [0; 1; 0; 0];
+
+  Pr = ss ([eye(m1,p)  ;
+            zeros(m2,p);
+            zeros(m3,p);
+            eye(p,p)   ]);
+
+  Pu1 = ss ([-eye(m1,p)  ;
+              zeros(m2,p);
+              eye(m3,p)  ;
+             -eye(p,p)   ]);
+
+  Pu2 = ss ([zeros(m1,m);
+             eye(m2,m)  ;
+             zeros(m3,m);
+             zeros(p,m) ]);
+
+  Pu = Pu1 * G  +  Pu2;
+
+  P = append (W1, W2, W3, eye (p, p)) * [Pr, Pu];
+
+endfunction
+
+
+function [W, p, m] = __adjust_weighting__ (W, s)
+
+  W = ss (W);
+  [p, m] = size (W);
+
+  if (m == 0 || m == s)               # model is empty or has s inputs
+    return;
+  elseif (m == 1)                     # model is SISO or SIMO
+    tmp = W;
+    for k = 2 : s
+      W = append (W, tmp);            # stack single-input model s times
+    endfor
+    [p, m] = size (W);                # weighting function now of correct size
+  else                                # model is MIMO or MISO
+    error ("augw: %s must have 1 or %d inputs", inputname (1), s);
+  endif 
+
+endfunction