c2d

% -*- texinfo -*-
% @deftypefn {Function File} {} c2d (@var{sys}, @var{opt}, @var{t})
% @deftypefnx {Function File} {} c2d (@var{sys}, @var{t})
%
% Converts the system data structure describing:
% @iftex
% @tex
% $$ \dot x = A_cx + B_cu $$
% @end tex
% @end iftex
% @ifinfo
% @example
% .
% x = Ac x + Bc u
% @end example
% @end ifinfo
% into a discrete time equivalent model:
% @iftex
% @tex
% $$ x_{n+1} = A_dx_n + B_du_n $$
% @end tex
% @end iftex
% @ifinfo
% @example
% x[n+1] = Ad x[n] + Bd u[n]
% @end example
% @end ifinfo
% via the matrix exponential or bilinear transform.
%
% @strong{Inputs}
% @table @var
% @item sys
% system data structure (may have both continuous time and discrete
% time subsystems)
% @item opt
% string argument; conversion option (optional argument;
% may be omitted as shown above)
% @table @code
% @item 'ex'
% use the matrix exponential (default)
% @item 'bi'
% use the bilinear transformation
% @iftex
% @tex
% $$ s = { 2(z-1) \over T(z+1) } $$
% @end tex
% @end iftex
% @ifinfo
% @example
%     2(z-1)
% s = -----
%     T(z+1)
% @end example
% @end ifinfo
% FIXME: This option exits with an error if @var{sys} is not purely
% continuous. (The @code{ex} option can handle mixed systems.)
% @item 'matched'
% Use the matched pole/zero equivalent transformation (currently only
% works for purely continuous @acronym{SISO} systems).
% @end table
% @item t
% sampling time; required if @var{sys} is purely continuous.
% 
% @strong{Note} that if the second argument is not a string, @code{c2d}
% assumes that the second argument is @var{t} and performs 
% appropriate argument checks.
% @end table
%
% @strong{Output}
% @table @var
% @item dsys 
% Discrete time equivalent via zero-order hold, sample each @var{t} sec.
% @end table
%
% This function adds the suffix  @code{_d}
% to the names of the new discrete states.
% @end deftypefn