% NOTES:
% For support, contact M. Peet, Arizona State University at mpeet@asu.edu
%
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% PIETOOLS - README
%
% Copyright (C)2019 M. Peet, S. Shivakumar
%
% 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, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
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%
% If you modify this code, document all changes carefully and include date
% authorship, and a brief description of modifications
%
% This file is packaged with PIETOOLS and contains License information, a
% list of all the files packaged with PIETOOLS and a brief description of
% the functions and scripts. If any of the following files are missing from
% the PIETOOLS folder, the toolbox may not function as expected. In that
% case, reinstall using the install script or contact sshivak@asu.edu or
% mpeet@asu.edu for support.
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% What is PIETOOLS?
% PIETOOLS is a free MATLAB toolbox for formulating and solving Linear PI
% Inequalities (LPIs) programs. PIETOOLS can be used to define 3-PI or 4-PI
% operators, declare 3-PI or 4-PI operators variables (postive semidefinite
% or indefinite), add operator inequality constraints, and solve LPI
% optimization problems. The interface is inspired by YALMIP and the program
% structure is based on that used by SOSTOOLS. By default the LPIs are solved
% using SeDuMi.
% What is a PIE?
% PIE stands for Partial Integral Equation and is an alternative
% representation for many commonly encountered classes of systems, including
% Ordinary Differential Equations (ODEs), Partial-Differential Equations
% (PDEs), Delay Differential Equations (DDEs), and Differential-Difference
% Equations (DDFs).
%
% The cool thing about PIEs is that, unlike PDEs and DDEs (which have lame
% boundary conditions, unbounded operators, and continuity constraints), PIEs
% are defined by the very slick linear algebra of 3/4 PI operators. This
% feature makes PIEs the representation of choice if you want to do anything
% computational with your beam equation, network model, reaction-diffusion
% equations, etc.
%
% Now, you may be wondering if you are going to lose anything by switching
% your PDE/DDE/DDF to a PIE. No! That would be awful. You may have been hurt
% in the past by people wrecking your lovely PDE/DDE/DDF using such barbaric
% tools as approximation via discretization, projection, mollification,
% regularization or Pade. However, let us assure you that using PIEs is
% completely safe. The PIE representation of a PDE/DDE/DDF is exact. The
% solutions are one-to-one, only the tools used for representation have
% improved.
%
% What can I do with PIETOOLS?
% The use of PIETOOLS is organized into 4 categories. These are:
% 1) Manipulation of 3-PI and 4-PI operators.
% 2) Constructing and Solving Linear PI Inequalities (LPIs).
% 3) Converting PDEs/DDEs/DDFs to PIEs.
% 4) Solving LPIs for Analysis and Control of PIEs.