--- /dev/null
+## 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