is_controllable

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{retval}, @var{u}] =} is_controllable (@var{sys}, @var{tol})
% @deftypefnx {Function File} {[@var{retval}, @var{u}] =} is_controllable (@var{a}, @var{b}, @var{tol})
% Logical check for system controllability.
%
% @strong{Inputs}
% @table @var
% @item sys
% system data structure
% @item a
% @itemx b
% @var{n} by @var{n}, @var{n} by @var{m} matrices, respectively
% @item tol
% optional roundoff parameter.  Default value: @code{10*eps}
% @end table
%
% @strong{Outputs}
% @table @var
% @item retval
% Logical flag; returns true (1) if the system @var{sys} or the
% pair (@var{a}, @var{b}) is controllable, whichever was passed as input
% arguments.
% @item u
% @var{u} is an orthogonal basis of the controllable subspace.
% @end table
%
% @strong{Method}
% Controllability is determined by applying Arnoldi iteration with
% complete re-orthogonalization to obtain an orthogonal basis of the
% Krylov subspace
% @example
% span ([b,a*b,...,a^@{n-1@}*b]).
% @end example
% The Arnoldi iteration is executed with @code{krylov} if the system
% has a single input; otherwise a block Arnoldi iteration is performed
% with @code{krylovb}.
% @seealso{size, rows, columns, length, ismatrix, isscalar, isvector, is_observable, is_stabilizable, is_detectable, krylov, krylovb}
% @end deftypefn