Mercurial > octave-nkf
view scripts/control/is_controllable.m @ 56:3cccff82b7a6
[project @ 1993-08-11 21:49:22 by jwe]
author | jwe |
---|---|
date | Wed, 11 Aug 1993 21:49:27 +0000 |
parents | e90ea9cbd4de |
children | f3c9042fd609 |
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function retval = is_controllable (a,b,tol) # usage: is_controllable (a,b{,tol}) # # Returns 1 if the pair (a, b) is controllable, or 0 if not. # # See also: size, rows, columns, length, is_matrix, is_scalar, is_vector # This should really use the method below, but I'm being lazy for now: # # Controllability is determined by applying Arnoldi iteration with # complete re-orthogonalization to obtain an orthogonal basis of the # Krylov subspace # n-1 # span ([b,a*b,...,a^ b]). # # tol is a roundoff paramter, set to 2*eps if omitted if (nargin == 2 || nargin == 3) n = is_square (a); [nr, nc] = size (b); if (n == 0 || n != nr || nc == 0) retval = 0; else m = b; tmp = b; for ii = 1:(n-1) tmp = a * tmp; m = [m, tmp]; endfor # If n is of any significant size, m will be low rank, so be careful! if (nargin == 3) if (is_scalar (tol)) retval = (rank (m, tol) == n); else error ("is_controllable: tol must be a scalar"); endif else retval = (rank (m) == n); endif endif else error ("usage: is_controllable (a, b)"); endif endfunction