Papers | Collaborators | Optimization Software | NCAlgebra

J. William Helton

Department of Mathematics
University of California San Diego
9500 Gilman Drive
La Jolla, California 92093-0112
Mailcode: 0112
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SLIDES Bill's talk at AIM2021.pdf

PAPERS of J W Helton and preprints pre mid 2011
Click on this will bring up a fairly recent pub list,
but the recent links n it have no substance. We just use arXiv now.

Bill's papers on arXiv:
PAPERS of J W Helton on arXiv

Our Focused Research Group in Convex Algebraic Geometry

An Eclectic Conference at UCSD:   Oct 2,3,4 of 2010


AIM09.pdf one per page one per page
AIM09p9.pdf 9 per page

Engineering Motivation for NC inequalities
Engineering Motivation for NC inequalities 6 per page
Book 1998
Classical Control Using H-infty Methods
By J. William Helton and Orlando Merino. SIAM, 1998.

Book 1999
Extending H-infty Control to Nonlinear Systems.
By J. William Helton and Matt James. SIAM, Dec. 1999.
This is a research monograph which focuses on measurement feedback control or, for those with less of an engineering pursuasion, on factoring nonlinear operators acting on L^2. It gives an outline of the subject and then it gives details of resesarch (mostly of the authors) over the last 4 years. The first part of the book should be good for the beginner and the book's interior is definitely on the bleeding edge. The lighthearted part is:
Contents, Intro, History and the First 3 Yards
Some Special cases and Factoring
Index and Bibliography
Formulas for Nonlinear Time Varying Control
Directions beyond the book; recent papers


The following software packages are currently available through anonymous ftp.


Our Non Commutative Algebra Package which runs under Mathematica is available from or better yet from the NCAlgebra Homepage. Getting it from us is better since our version is much more recent. A Noncommutative Gröbner Basis Package NCGB which makes use of the NCAlgebra package is available too NCAlgebra Homepage. For complaints or to report really wild NC Expereiences there is our email

Optimization Over Analytic Functions
There are several software packages available for optimization over analytic functions which were used to run examples in the book Classical Control Using H-infty Methods.

Chemical Reaction Equation Software
The Mathematica files provided on this page contain software for dealing with equations that come from chemical reaction networks. These equations are ordinary differential equations of the form dx/dt=f(x)=S v(x); some properties of these equations relating to steady states are often discernable from the Jacobian, f ', of f. The software is good for analysing sign patterns of f', signs of the coefficients of the polynomial det f'(x).
Also there are commands which express S v(x) in another conventional form YA monomials(x), used in deficiency theory.

A list of the coauthors of Bill's older papers.

Amusing to the trade:
Mathematical Theory of Networks and Systems (MTNS) HISTORY

An address by Hilbert

Noncommutative Moment Matrix of Degree 2

These are here so Bill can always find them.

M120B SPRING 2015 Web page >

M120A FALL 2013 Web page >

M241A Fall 2013 Web page >

M120B WINTER 2014 Web page >

M241A FALL 2012 Handout
M247A Real Topics, Web page >

M20C WINTER 2012 Web page >
Math 20D Spring 2011 Webpage

M20F Winter 2009 Web page >

M120A Fall 2008 Web page >

M241A Fall 2008 Web page >

Topics M247B Fall and Winter 2008 Web page >
M247A   Spring 2004
Homework for M130B 2004


1. Tutorial Workshop:on Real Algebraic Geometry, Polynomial Optimization and Linear Matrix Inequalities (LMIPO) At UCSD     March 22-25   2009
2. BANFF 2009
3. AIM 2009

Thanks for financial support to the NSF via grant DMS 1500835 and to the Ford Motor Co..

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