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# are

## PURPOSE

% Solve the Algebraic Riccati Equation

## SYNOPSIS

function x = are (a, b, c, opt)

## DESCRIPTION

% -*- texinfo -*-
% @deftypefn {Function File} {@var{x} =} are (@var{a}, @var{b}, @var{c}, @var{opt})
% Solve the Algebraic Riccati Equation
% @iftex
% @tex
% \$\$
% A^TX + XA - XBX + C = 0
% \$\$
% @end tex
% @end iftex
% @ifinfo
% @example
% a' * x + x * a - x * b * x + c = 0
% @end example
% @end ifinfo
%
% @strong{Inputs}
% @noindent
% for identically dimensioned square matrices
% @table @var
% @item a
% @var{n} by @var{n} matrix;
% @item b
%   @var{n} by @var{n} matrix or @var{n} by @var{m} matrix; in the latter case
%   @var{b} is replaced by @math{b:=b*b'};
% @item c
%   @var{n} by @var{n} matrix or @var{p} by @var{m} matrix; in the latter case
%   @var{c} is replaced by @math{c:=c'*c};
% @item opt
% (optional argument; default = @code{'B'}):
% String option passed to @code{balance} prior to ordered Schur decomposition.
% @end table
%
% @strong{Output}
% @table @var
% @item x
% solution of the @acronym{ARE}.
% @end table
%
% @strong{Method}
% Laub's Schur method (@acronym{IEEE} Transactions on
% Automatic Control, 1979) is applied to the appropriate Hamiltonian
% matrix.
% @seealso{balance, dare}
% @end deftypefn

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• analdemo % Octave Controls toolbox demo: State Space analysis demo
• h2syn % Design
• hinfsyn_chk % Called by @code{hinfsyn} to see if gain @var{g} satisfies conditions in
• lqr % construct the linear quadratic regulator for the continuous time system

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