sosposmatrvar.m

function [sos,Q] = sosposmatrvar(sos,n,d,vars)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SOSPOSMATRVAR(prog,n,d,vars)
%
% This program declares a symbolic positive scalar semidefinite matrix P of
% size nxn which is positive semidefinite for all values of the variables.
% The matrix has the form
% [Z   ]^T   [Z   ]
% [ Z  ]   Q [ Z  ]
% [  Z ]     [  Z ]
% [   Z]     [   Z], Q>0
%
%Where $Z$ is the vector of monomials in vaiables vars of degree d/2 or
%less. Q is a positive semidefinite matrix.
%
% INPUTS:
%
% prog - The SOS program to which to attach the variable
% n - dimension of matrix variable
% d - degree of polynomial entries of the matrix
% vars - variables in the entries of the polynomial
%

%
% This file is part of SOSTOOLS - Sum of Squares Toolbox ver 4.00.
%
% Copyright (C)2002, 2004, 2013, 2016, 2018, 2021  
%                                      A. Papachristodoulou (1), J. Anderson (1),
%                                      G. Valmorbida (2), S. Prajna (3), 
%                                      P. Seiler (4), P. A. Parrilo (5),
%                                      M. Peet (6), D. Jagt (6)
% (1) Department of Engineering Science, University of Oxford, Oxford, U.K.
% (2) Laboratoire de Signaux et Systmes, CentraleSupelec, Gif sur Yvette,
%     91192, France
% (3) Control and Dynamical Systems - California Institute of Technology,
%     Pasadena, CA 91125, USA.
% (4) Aerospace and Engineering Mechanics Department, University of
%     Minnesota, Minneapolis, MN 55455-0153, USA.
% (5) Laboratory for Information and Decision Systems, M.I.T.,
%     Massachusetts, MA 02139-4307
% (6) Cybernetic Systems and Controls Laboratory, Arizona State University,
%     Tempe, AZ 85287-6106, USA.
%
% Send bug reports and feedback to: sostools@cds.caltech.edu
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Change log and developer notes
%
% original coding - MMP, 2013
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if ~even(d)
    error(['Degree of the SOS Polynomial Matrix should be even']);
end
if ~isvalid(vars)
    error(['vars must be a polynomial variable']);
end

%    Z=monomials_nd(vars,0:ceil(d/2),1);
Z=monomials(vars,0:ceil(d/2));


[sos,Q]=sosquadvar(sos,Z,Z,n,n,'pos');