Quantitative Local Analysis of Nonlinear Systems
Using SumofSquares
Decompositions
2009 American Control Conference
St. Louis, Missouri, USA
June 9, 2009
Andrew Packard
University of California, Berkeley
Gary Balas
University of Minnesota
Peter Seiler
Honeywell Laboratories
Ufuk Topcu
California Institute of Technology
Presentation Slides
Introduction.
Main presentation.
MATLAB Software

SeDuMi is maintained by Lehigh University.
See their website for
downloads, installation instructions, etc.

You can download all the nonlinear analysis software (except SeDuMi) in one
package here.

You can also download the individual packages

sosaddpath.m. Script file to
configure the MATLAB path for these packages.

Multipoly Packaged used to
represent multivariate polynomials.

Polysys. Package used to
model, simulate, and analyze nonlinear systems with polynomial
dynamics.

Worstcase. Package to compute
the induced gain of nonlinear systems using an iterative
algorithm.

SOSOpt. General SOS optimization utility.

Other nonlinear analysis code. The rest of the
routines discussed in the workshop.
MATLAB Diary Files
Multipoly demo.
References
References.
Details for the software packages listed above can be found in the
following publications:

J. Tierno, R. Murray, and J. C. Doyle. "An efficient algorithm for
performance analysis of nonlinear control systems." Proceedings of the
1995 American Control Conference, pp. 27172721.

P. A. Parrilo. Structured semidefinite programs and semialgebraic
geometry methods in robustness and optimization. Ph.D.
Dissertation, California Institute of Technology, 2000. (pdf)

W. Tan. Nonlinear control analysis and synthesis using
SumofSquares programming. Ph.D. Dissertation, University of
California, Berkeley, 2006. (pdf )

U. Topcu. Quantitative local analysis of nonlinear systems. Ph.D.
Dissertation, University of California, Berkeley, 2008. (pdf)