/usr/share/octave/packages/control-2.6.2/@ss/__sys_connect__.m is in octave-control 2.6.2-1build1.
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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 | ## Copyright (C) 2009-2014 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{retsys} =} __sys_connect__ (@var{sys}, @var{M})
## This function is part of the Model Abstraction Layer. No argument checking.
## For internal use only.
## @example
## @group
## Problem: Solve the system equations of
## .
## E x(t) = A x(t) + B e(t)
##
## y(t) = C x(t) + D e(t)
##
## e(t) = u(t) + M y(t)
##
## in order to build
## .
## K x(t) = F x(t) + G u(t)
##
## y(t) = H x(t) + J u(t)
##
## Solution: Laplace Transformation
## E s X(s) = A X(s) + B U(s) + B M Y(s) [1]
##
## Y(s) = C X(s) + D U(s) + D M Y(s) [2]
##
## solve [2] for Y(s)
## Y(s) = [I - D M]^(-1) C X(s) + [I - D M]^(-1) D U(s)
##
## substitute Z = [I - D M]^(-1)
## Y(s) = Z C X(s) + Z D U(s) [3]
##
## insert [3] in [1], solve for X(s)
## X(s) = [s E - (A + B M Z C)]^(-1) (B + B M Z D) U(s) [4]
##
## inserting [4] in [3] finally yields
## Y(s) = Z C [s E - (A + B M Z C)]^(-1) (B + B M Z D) U(s) + Z D U(s)
## \ / | \_____ _____/ \_____ _____/ \ /
## H K F G J
## @end group
## @end example
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: September 2009
## Version: 0.2
function sys = __sys_connect__ (sys, m)
a = sys.a;
b = sys.b;
c = sys.c;
d = sys.d;
z = eye (rows (d)) - d*m;
if (rcond (z) < eps) # check for singularity
error ("ss: sys_connect: (I - D*M) singular");
endif
z = inv (z);
sys.a = a + b*m*z*c; # F
sys.b = b + b*m*z*d; # G
sys.c = z*c; # H
sys.d = z*d; # J
## sys.e remains constant: [] for ss models, e for dss models
endfunction
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