% -*- texinfo -*-
% @deftypefn {Function File} {[@var{retval}, @var{dgkf_struct} ] =} is_dgkf (@var{asys}, @var{nu}, @var{ny}, @var{tol} )
% Determine whether a continuous time state space system meets
% assumptions of @acronym{DGKF} algorithm.
% Partitions system into:
% @example
% [dx/dt] [A | Bw Bu ][w]
% [ z ] = [Cz | Dzw Dzu ][u]
% [ y ] [Cy | Dyw Dyu ]
% @end example
% or similar discrete-time system.
% If necessary, orthogonal transformations @var{qw}, @var{qz} and nonsingular
% transformations @var{ru}, @var{ry} are applied to respective vectors
% @var{w}, @var{z}, @var{u}, @var{y} in order to satisfy @acronym{DGKF} assumptions.
% Loop shifting is used if @var{dyu} block is nonzero.
%
% @strong{Inputs}
% @table @var
% @item asys
% system data structure
% @item nu
% number of controlled inputs
% @item ny
% number of measured outputs
% @item tol
% threshold for 0; default: 200*@code{eps}.
% @end table
% @strong{Outputs}
% @table @var
% @item retval
% true(1) if system passes check, false(0) otherwise
% @item dgkf_struct
% data structure of @command{is_dgkf} results. Entries:
% @table @var
% @item nw
% @itemx nz
% dimensions of @var{w}, @var{z}
% @item a
% system @math{A} matrix
% @item bw
% (@var{n} x @var{nw}) @var{qw}-transformed disturbance input matrix
% @item bu
% (@var{n} x @var{nu}) @var{ru}-transformed controlled input matrix;
%
% @math{B = [Bw Bu]}
% @item cz
% (@var{nz} x @var{n}) Qz-transformed error output matrix
% @item cy
% (@var{ny} x @var{n}) @var{ry}-transformed measured output matrix
%
% @math{C = [Cz; Cy]}
% @item dzu
% @item dyw
% off-diagonal blocks of transformed system @math{D} matrix that enter
% @var{z}, @var{y} from @var{u}, @var{w} respectively
% @item ru
% controlled input transformation matrix
% @item ry
% observed output transformation matrix
% @item dyu_nz
% nonzero if the @var{dyu} block is nonzero.
% @item dyu
% untransformed @var{dyu} block
% @item dflg
% nonzero if the system is discrete-time
% @end table
% @end table
% @code{is_dgkf} exits with an error if the system is mixed
% discrete/continuous.
%
% @strong{References}
% @table @strong
% @item [1]
% Doyle, Glover, Khargonekar, Francis, @cite{State Space Solutions to Standard}
% @iftex
% @tex
% $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
% @end tex
% @end iftex
% @ifinfo
% @cite{H-2 and H-infinity}
% @end ifinfo
% @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
% @item [2]
% Maciejowksi, J.M., @cite{Multivariable Feedback Design}, Addison-Wesley, 1989.
% @end table
% @end deftypefn