NEW: RESEARCH POSITIONS AVAILABLE
My research goal is to develop tools for the analysis and control of nonlinear ordinary equations and also some kinds of partial differential equations. I am interested in applications in communications networks with nonlinear and decentralized dynamics, sparse interconnection and delayed feedback. I am currently working on the use of semidefinite programming for stability analysis of Chronic Myelogenous Leukemia. I have developed some matlab toolboxes which can be used for analysis of differential equations with delays. For a detailed description of my research, please refer to my cv or extended research statement.
Thesis:
Stanford University, Department of Aeronautics and Astronautics
Stability and Control of Functional Differential Equations
Defended March 15, 2006.
Thesis - [arXiv:math/0607144v1] [.pdf] [.ps]
Defense Talk - [.pdf] [.ps]
Journal Articles:
M. M. Peet
Exponentially Stable Nonlinear Systems have Polynomial Lyapunov Functions on Bounded Regions
IEEE Transactions on Automatic Control, Vol 52, No. 5, May 2009
[arXiv:0707.0218v1] [.pdf] [.ps]Summary: A proof that one can use only polynomial Lyapunov functions to prove exponential stability of ordinary differential equations with no additional conservatism.
M. M. Peet, A. Papachristodoulou and S. Lall
Positive Forms and Stability of Linear Time-Delay Systems
SIAM Journal on Control and Optimization, Vol 47, No. 6
[arXiv:0707.0230v1] [.pdf] [.ps]Summary: A framework for using semidefinite programming to construct Lyapunov functions for infinite-dimensional systems (i.e. delay-differential and partial differential equations).
A. Papachristodoulou, M. M. Peet and S. Lall
Stabiltiy Analysis of Nonlinear Time Delay Systems
IEEE Transactions on Automatic Control, Vol 52, No. 5, May 2009
[arXiv] [.pdf] [.ps]Summary: An overview of how the methods from `` Positive Forms and Stability of Linear Time-Delay Systems'' can be applied to nonlinear time-delay systems.
M. M. Peet and S. Lall
Stability Analysis of a Nonlinear Model of Internet Congestion Control with Delay
IEEE Transactions on Automatic Control, Vol. 52, No. 3, March 2007
[arXiv] [.pdf] [.ps]
Technical Report with Detailed Proofs [arXiv] [.pdf] [.ps]Summary: An exact characterization of the hybrid, nonlinear, and time-delayed model and region of stability for a popular internet congestion control protocol.
Book Chapters:
M. M. Peet, C. Bonnet, and H. Ozbay
SOS Methods for Stability Analysis of Neutral Differential Systems
Springer Lecture Notes in Control and Information Sciences. To Appear.
Preliminary version appeared at MTNS, 2008.
[arXiv] [.pdf] [.ps]A. Papachristodoulou and M. M. Peet
SOS Methods for Nonlinear Delayed Models in Biology and Networking
Springer Lecture Notes in Control and Information Sciences. To Appear.
[arXiv] [.pdf] [.ps]
Conference Papers:
M. M. Peet and A. Papachristodoulou
Using Polynomial Semi-Separable Kernels to Construct Infinite-Dimensional Lyapunov Functions
47th IEEE Conference on Decision and Control, Cancun, Mexico. December 9-11, 2008.
[arXiv] [.pdf] [.ps]M. M. Peet, H. Ozbay, and C. Bonnet
SOS for Delay-Dependent Stability of Neutral Differential Equations
Mathematical Theory of Networks and Systems, Blacksburg, VA. July 28-Aug. 1, 2008.
[arXiv] [.pdf] [.ps]M. M. Peet, and P.-A. Bliman
The Weierstrass Approximation Theorem on Linear Varieties: Polynomial Lyapunov Functionals for Delayed Systems
Mathematical Theory of Networks and Systems, Blacksburg, VA. July 28-Aug. 1, 2008.
Preliminary version appeared at the workshop TDS 2007.
[arXiv] [.pdf] [.ps]A. Papachristodoulou and M. M. Peet
Global Stability Analysis of Primal Internet Congestion Control Schemes with Heterogeneous Delays
IFAC World Congress. Seoul, South Korea. June 6-11, 2008.
[arXiv] [.pdf] [.ps]M. M. Peet, and P.-A. Bliman
Polynomial Lyapunov Functions for Exponential Stability of Nonlinear Systems on Bounded Regions
IFAC World Congress. Seoul, South Korea. June 6-11, 2008.
Preliminary version appeared at Allerton, 2007.
[arXiv] [.pdf] [.ps]A. Papachristodoulou, M. M. Peet, and S.-I. Niculescu
Stability Analysis of Linear Systems with Time-Varying Delays: Delay Uncertainty and Quenching
46th IEEE Conference on Decision and Control, New Orleans, LA. December 12-14, 2007.
[arXiv] [.pdf] [.ps]M. M. Peet and A. Papachristodoulou
Positivity of Kernel Functions for Systems with Communication Delay
46th IEEE Conference on Decision and Control, New Orleans, LA. December 12-14, 2007.
Preliminary version appeared at the Conference de la SMAI su l'optimisation et la decision, 2007
[arXiv] [.pdf] [.ps]M. M. Peet
Exponentially Stable Nonlinear Systems have Polynomial Lyapunov Functions on Bounded Regions
45th annual Allerton Conference on Communication, Control, and Computing. Monticello, IL. Sept 26-28, 2007.
[arXiv] [.pdf] [.ps]C. Bonnet and M. M. Peet
Using the Positivstellensatz for Stability Analysis of Neutral Delay Systems in the Frequency Domain
7th IFAC Workshop on Time-Delay Systems. Nantes, France. Sept. 17-19, 2007.
[arXiv] [.pdf] [.ps]M. M. Peet and P.-A. Bliman
An Extension of the Weierstrass Theorem to Linear Varieties: Application to Delay Systems
7th IFAC Workshop on Time-Delay Systems. Nantes, France. Sept. 17-19, 2007.
[arXiv] [.pdf] [.ps]M. M. Peet and C. Bonnet
Stability and Computation of Roots in Delayed Systems of the Neutral Type
IFAC Workshop on Control of Distributed Parameter Systems. Namur, Belgium. July 22-27, 2007. pp. 49-50.
[arXiv] [.pdf] [.ps]M. M. Peet
On Positive Quadratic Forms and Stability of Linear Systems
Conference de la SMAI su l'optimisation et la decision, April 18-20, 2007.
[arXiv] [.pdf] [.ps]M. M. Peet, A. Papachristodoulou and S. Lall
Positive Forms and the Stability of Linear Time-Delay Systems
Proceedings of the 45th IEEE Conference on Decision and Control(CDC), December 13-15, 2006. pp. 187-193.
[arXiv] [.pdf] [.ps]A. Papachristodoulou and M. M. Peet
On the Analysis of Systems Described by Classes of Partial Differential Equations
Proceedings of the 45th IEEE Conference on Decision and Control(CDC), December 13-15, 2006. pp. 747-752.
[arXiv] [.pdf] [.ps]A. Papachristodoulou, M. M. Peet and S. Lall
Constructing Lyapunov-Krasovskii Functionals for Linear Time Delay Systems
Proceedings of the American Control Conference, pp. 2845-2850, June 2005.
[arXiv] [.pdf] [.ps]M. M. Peet and S. Lall
On Global Stability of Internet Congestion Control
Proceedings of the 43rd IEEE Conference on Decision and Control(CDC), pp. 1035-1041, December 2004.
[arXiv] [.pdf] [.ps]M. M. Peet and S. Lall
Constructing Lyapunov Functions for Nonlinear Delay-Differential Equations using Semidefinite Programming
Proceedings of the 6th IFAC Symposium on Nonlinear Control Systems(NOLCOS), pp. 381-385, August 2004.
[arXiv] [.pdf] [.ps]
Home Phone: +1 630-468-2880
Mobile: +1 630-272-4451
Home Address:
938 South Grant St.
Hinsdale, IL 60521
USA
Work Phone: +1 312-567-3220
Work Address:
10 West 32nd Street
E1-252B
Chicago, IL 60616
USA
Email 1 : mmpeet@gmail.com
Email 2 : mpeet@iit.edu