PIETOOLS: A Matlab Toolbox for Manipulation and Optimization of Partial Integral Operators

Sachin Shivakumar, Amritam Das, Matthew M. Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations


In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar, for which standard MATLAB matrix operation syntax (e.g. +, ' etc.) is defined. PI operators are a generalization of bounded linear operators on infinite-dimensional spaces that form a-subalgebra with two binary operations (addition and composition) on the space × L2. These operators frequently appear in analysis and control of infinite-dimensional systems such as Partial Differential Equations (PDE) and Timedelay systems (TDS). Furthermore, PIETOOLS can: declare opvar decision variables, add operator positivity constraints, declare an objective function, and solve the resulting optimization problem using a syntax similar to the sdpvar class in YALMIP. Use of the resulting Linear Operator Inequalities (LOI) are demonstrated on several examples, including stability analysis of a PDE, bounding operator norms, and verifying integral inequalities. The result is that PIETOOLS, packaged with SOSTOOLS and MULTIPOLY, offers a scalable, user-friendly and computationally efficient toolbox for parsing, performing algebraic operations, setting up and solving convex optimization problems on PI operators.

Original languageEnglish (US)
Title of host publication2020 American Control Conference, ACC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538682661
StatePublished - Jul 2020
Event2020 American Control Conference, ACC 2020 - Denver, United States
Duration: Jul 1 2020Jul 3 2020

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2020 American Control Conference, ACC 2020
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'PIETOOLS: A Matlab Toolbox for Manipulation and Optimization of Partial Integral Operators'. Together they form a unique fingerprint.

Cite this