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# gram

## PURPOSE

% @code{gram (@var{sys}, 'c')} returns the controllability gramian of

## SYNOPSIS

function W = gram (argin1, argin2)

## DESCRIPTION

```% -*- texinfo -*-
% @deftypefn {Function File} {@var{W} =} gram (@var{sys}, @var{mode})
% @deftypefnx {Function File} {@var{Wc} =} gram (@var{a}, @var{b})
% @code{gram (@var{sys}, 'c')} returns the controllability gramian of
% the (continuous- or discrete-time) system @var{sys}.
% @code{gram (@var{sys}, 'o')} returns the observability gramian of the
% (continuous- or discrete-time) system @var{sys}.
% @code{gram (@var{a}, @var{b})} returns the controllability gramian
% @var{Wc} of the continuous-time system @math{dx/dt = a x + b u};
% i.e., @var{Wc} satisfies @math{a Wc + m Wc' + b b' = 0}.
%
% @end deftypefn```

## CROSS-REFERENCE INFORMATION

This function calls:
• dlyap % Solve the discrete-time Lyapunov equation
• is_stable % Returns 1 if the matrix @var{a} or the system @var{sys}
• isct % Return true if the LTI system @var{sys} is continuous-time, false otherwise.
• isdt % Return true if the LTI system @var{sys} is discrete-time, false otherwise.
• lyap % Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart
This function is called by:
• analdemo % Octave Controls toolbox demo: State Space analysis demo
• balreal % Balanced realization of the continuous-time LTI system @var{sys}.
• dgram % Return controllability gramian of discrete time system

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