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# lyap

## PURPOSE

% Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart

## SYNOPSIS

function x = lyap (a, b, c)

## DESCRIPTION

```% -*- texinfo -*-
% @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c})
% @deftypefnx {Function File} {} lyap (@var{a}, @var{b})
% Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart
% algorithm (Communications of the @acronym{ACM}, 1972).
%
% If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns
% the solution of the  Sylvester equation
% @iftex
% @tex
%   \$\$ A X + X B + C = 0 \$\$
% @end tex
% @end iftex
% @ifinfo
% @example
%     a x + x b + c = 0
% @end example
% @end ifinfo
% If only @code{(a, b)} are specified, then @command{lyap} returns the
% solution of the Lyapunov equation
% @iftex
% @tex
%   \$\$ A^T X + X A + B = 0 \$\$
% @end tex
% @end iftex
% @ifinfo
% @example
%     a' x + x a + b = 0
% @end example
% @end ifinfo
% If @var{b} is not square, then @code{lyap} returns the solution of either
% @iftex
% @tex
%   \$\$ A^T X + X A + B^T B = 0 \$\$
% @end tex
% @end iftex
% @ifinfo
% @example
%     a' x + x a + b' b = 0
% @end example
% @end ifinfo
% @noindent
% or
% @iftex
% @tex
%   \$\$ A X + X A^T + B B^T = 0 \$\$
% @end tex
% @end iftex
% @ifinfo
% @example
%     a x + x a' + b b' = 0
% @end example
% @end ifinfo
% @noindent
% whichever is appropriate.
%
% Solves by using the Bartels-Stewart algorithm (1972).
% @end deftypefn```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• gram % @code{gram (@var{sys}, 'c')} returns the controllability gramian of
• h2norm % Computes the

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