Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / isstabilizable.m

diff --git a/octave_packages/control-2.3.52/isstabilizable.m b/octave_packages/control-2.3.52/isstabilizable.m
new file mode 100644 (file)
index 0000000..8e2377c
--- /dev/null
+++ b/octave_packages/control-2.3.52/isstabilizable.m
@@ -0,0 +1,135 @@
+## Copyright (C) 2009, 2010, 2012   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{bool} =} isstabilizable (@var{sys})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{sys}, @var{tol})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{tol})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{tol})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{[]}, @var{dflg})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{[]}, @var{dflg})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{tol}, @var{dflg})
+## @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{tol}, @var{dflg})
+## Logical check for system stabilizability.
+## All unstable modes must be controllable or all uncontrollable states must be stable.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## LTI system.
+## @item a
+## State transition matrix.
+## @item b
+## Input matrix.
+## @item e
+## Descriptor matrix.
+## If @var{e} is empty @code{[]} or not specified, an identity matrix is assumed.
+## @item tol
+## Optional tolerance for stability.  Default value is 0.
+## @item dflg = 0
+## Matrices (@var{a}, @var{b}) are part of a continuous-time system.  Default Value.
+## @item dflg = 1
+## Matrices (@var{a}, @var{b}) are part of a discrete-time system.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item bool = 0
+## System is not stabilizable.
+## @item bool = 1
+## System is stabilizable.
+## @end table
+##
+## @strong{Algorithm}@*
+## Uses SLICOT AB01OD and TG01HD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+## @example
+## @group
+## * Calculate staircase form (SLICOT AB01OD)
+## * Extract unobservable part of state transition matrix
+## * Calculate eigenvalues of unobservable part
+## * Check whether
+##   real (ev) < -tol*(1 + abs (ev))   continuous-time
+##   abs (ev) < 1 - tol                discrete-time
+## @end group
+## @end example
+## @seealso{isdetectable, isstable, isctrb, isobsv}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.4
+
+function bool = isstabilizable (a, b = [], e = [], tol = [], dflg = 0)
+
+  if (nargin < 1 || nargin > 5)
+    print_usage ();
+  elseif (isa (a, "lti"))  # isstabilizable (sys), isstabilizable (sys, tol)
+    if (nargin > 2)
+      print_usage ();
+    endif
+    tol = b;
+    dflg = ! isct (a);
+    [a, b, c, d, e] = dssdata (a, []);
+  elseif (nargin == 1)     # isstabilizable (a, b, ...)
+    print_usage ();
+  elseif (! is_real_square_matrix (a) || rows (a) != rows (b))
+    error ("isstabilizable: a must be square and conformal to b");
+  elseif (! isempty (e) && (! is_real_square_matrix (e) || ! size_equal (a, e)))
+    error ("isstabilizable: e must be square and conformal to a");
+  endif
+
+  if (isempty (tol))
+    tol = 0;               # default tolerance
+  elseif (! is_real_scalar (tol))
+    error ("isstabilizable: tol must be a real scalar");
+  endif
+
+  if (isempty (e))
+    ## controllability staircase form
+    [ac, ~, ~, ncont] = slab01od (a, b, tol);
+
+    ## extract uncontrollable part of staircase form
+    uncont_idx = ncont+1 : rows (a);
+    auncont = ac(uncont_idx, uncont_idx);
+
+    ## calculate poles of uncontrollable part
+    pol = eig (auncont);
+  else
+    ## controllability staircase form - output matrix c has no influence
+    [ac, ec, ~, ~, ~, ~, ncont] = sltg01hd (a, e, b, zeros (1, columns (a)), tol);
+
+    ## extract uncontrollable part of staircase form
+    uncont_idx = ncont+1 : rows (a);
+    auncont = ac(uncont_idx, uncont_idx);
+    euncont = ec(uncont_idx, uncont_idx);
+
+    ## calculate poles of uncontrollable part
+    pol = eig (auncont, euncont);
+    
+    ## remove infinite poles
+    tolinf = norm ([auncont, euncont], 2);
+    idx = find (abs (pol) < tolinf/eps);
+    pol = pol(idx);
+  endif
+
+  ## check whether uncontrollable poles are stable
+  bool = __is_stable__ (pol, ! dflg, tol);
+
+endfunction