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:
R. Kamyar, M. M. Peet and Y. Peet
Solving Large-Scale Robust Control Problems by Exploiting the Parallel Structure of Polya's Theorem
Submitted to IEEE Transactions on Automatic Control, 2011
[arXiv] [.pdf] [.ps]Summary: We develop a parallel algorithm for optimization of positive polynomials which has fixed complexity with respect to per-core memory, communication and computation. We then use cluster computing and supercomputing to analyze robust stability of state-space systems with parametric uncertainty and 100+ states.
M. M. Peet and A. Papachristodoulou
A Converse Sum-of-Squares Lyapunov Result with a Degree Bound
To Appear in IEEE Transactions on Automatic Control
[arXiv] [.pdf] [.ps]Summary: We show that exponential stability of a nonlinear system implies the existence of a Lyapunov function which is SOS. We give a degree bound for the Lyapunov function.
A. Seuret and M. M. Peet
Stability Analysis of Sampled-Data Systems using Sum-of-Squares
Submitted to Automatica, 2011
[arXiv] [.pdf] [.ps]Summary: Sampled-Data Systems are modeled as continuous-time plants coupled with a controller which updates at discrete, unpredictable times. We develop Lyapunov theory for these mixed discrete-continuous dynamics and use Sum-of-Squares to construct proofs of stability and exponential convergence.
Y. Zhang, M. M. Peet and K. Gu
Reducing the Complexity of the Sum-of-Squares Test for Stability of Delayed Linear Systems
IEEE Transactions on Automatic Control, Vol 56, No. 1, Jan. 2011
[arXiv] [.pdf] [.ps]Summary: We use recently developed converse Lyapunov theory to reduce the complexity of the SOS test by several orders of magnitude for systems with few delays.
M. M. Peet and P.-A. Bliman
On the Conservatism of the Sum-of-Squares Method for Analysis of Time-Delayed Systems
Automatica, Vol. 47, No. 11, Nov. 2011
[arXiv] [.pdf] [.ps]Summary: A converse Lyapunov result showing the existence of polynomial Lyapunov-Krasovskii functionals for stability of linear time-delay systems. Also a proof that the Weierstrass approximation theorem holds on linear varieties of continuous functions.
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, 2009
[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
Analysis of Polynomial Systems with Time Delays via the Sum of Squares Decomposition
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:
Y. Zhang, M. M. Peet and K. Gu
Accelerating Convergence of Sum-of-Squares Stability Analysis of Coupled Differential-Difference Equations
To Appear in "Time Delay Systems - Methods, Applications and New Trends'', Springer Lecture Notes in Control and Information Sciences.
[arXiv] [.pdf] [.ps]M. M. Peet, C. Bonnet, and H. Ozbay
SOS Methods for Stability Analysis of Neutral Differential Systems
in "Topics in Time Delay Systems: Analysis, Algorithms and Control'', Springer Lecture Notes in Control and Information Sciences.
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
in "Topics in Time Delay Systems: Analysis, Algorithms and Control', Springer Lecture Notes in Control and Information Sciences.
[arXiv] [.pdf] [.ps]
Conference Papers:
R. Kamyar and M. M. Peet
Solving Large-Scale Robust Control Problems by Exploiting the Parallel Structure of Polya's Theorem
Submitted to ACC 2012.
[arXiv] [.pdf] [.ps]M. M. Peet, P. Kim and P. Lee
Biological Circuit Models of Immune Regulatory Response: A Decentralized Control System
50th IEEE Conference on Decision and Control, Orlando, FL. December 12-16, 2011.
[arXiv] [.pdf] [.ps]A. Gahlawat and M. M. Peet
Designing Observer-Based Controllers for PDE systems: A Heat-Conducting Rod With Point Observation and Boundary Control
50th IEEE Conference on Decision and Control, Orlando, FL. December 12-16, 2011.
[arXiv] [.pdf] [.ps]A. Seuret and M. M. Peet
SOS for Sampled Data Systems
Proceedings of the IFAC World Congress, 2011.
[arXiv] [.pdf] [.ps]A. Gahlawat, M. M. Peet and E. Witrant
Control and Verification of the Safety-Factor Profile in Tokamaks Using Sum-of-Squares Polynomials
Proceedings of the IFAC World Congress, 2011.
[arXiv] [.pdf] [.ps]M. M. Peet and A. Papachristodoulou
A Converse Sum-of-Squares Lyapunov Result: An Existence Proof Based on the Picard Iteration
49th IEEE Conference on Decision and Control, Atlanta, GA. December 15-17, 2010.
[arXiv] [.pdf] [.ps]Y. Zhang, M. M. Peet and K. Gu
Reducing the Computational Cost of the Sum-of-Squares Stability Test for Time-Delayed Systems
Proceedings of the American Control Conference, Baltimore, MD. June 30-July 2, 2010.
[arXiv] [.pdf] [.ps]M. M. Peet and Y. V. Peet
A Parallel-Computing Solution for Optimization of Polynomials
Proceedings of the American Control Conference, Baltimore, MD. June 30-July 2, 2010.
[arXiv] [.pdf] [.ps]Y. Zhang and M. M. Peet and K. Gu
Accelerating Convergence of Sum-of-Square Formulation for Lyapunov-Krasovskii Stability Analysis of Coupled Differential-Difference Equations
9th IFAC Workshop on Time-Delay Systems. Prague, Czech Republic. June 7-9, 2010.
[arXiv] [.pdf] [.ps]M. M. Peet
A Bound on the Continuity of Solutions and Converse Lyapunov Functions
48th IEEE Conference on Decision and Control, Shanghai, China. December 16-18, 2009.
[arXiv] [.pdf] [.ps]M. M. Peet and A. Papachristodoulou
Inverses of Positive Linear Operators and State Feedback Design for Time-Delay Systems
8th IFAC Workshop on Time-Delay Systems. Siniai, Romania. Sept. 1-3, 2009.
[arXiv] [.pdf] [.ps]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: +1 224-260-8023
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Email 1 : mmpeet@gmail.com
Email 2 : mpeet@iit.edu