• 733 Citations
  • 16 h-Index
20042020
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Research Output 2004 2019

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2019

A New State-Space Representation for Coupled PDEs and Scalable Lyapunov Stability Analysis in the SOS Framework

Peet, M., Jan 18 2019, 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., p. 545-550 6 p. 8619025. (Proceedings of the IEEE Conference on Decision and Control; vol. 2018-December).

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

State-space Representation
Lyapunov Stability
Partial differential equations
Stability Analysis
Partial differential equation

Decentralized Control of Distributed Actuation in a Segmented Soft Robot Arm

Doroudchi, A., Shivakumar, S., Fisher, R. E., Marvi, H., Aukes, D., He, X., Berman, S. & Peet, M., Jan 18 2019, 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., p. 7002-7009 8 p. 8619036. (Proceedings of the IEEE Conference on Decision and Control; vol. 2018-December).

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

Decentralized control
Decentralized Control
Robot
Robots
Controller

Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems

Colbert, B. K. & Peet, M., Jan 18 2019, 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., p. 2341-2347 7 p. 8618959. (Proceedings of the IEEE Conference on Decision and Control; vol. 2018-December).

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

Lyapunov functions
Nonlinear systems
Nonlinear Systems
Trajectories
Trajectory
2018

A Convex Reformulation of the Controller Synthesis Problem for Infinite-Dimensional Systems using Linear Operator Inequalities (LOIs) with Application to MIMO Multi-Delay Systems

Peet, M., Aug 9 2018, 2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., Vol. 2018-June. p. 3322-3329 8 p. 8430836

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

MIMO systems
Controllers
Convex optimization

Combining SOS with Branch and Bound to Isolate Global Solutions of Polynomial Optimization Problems

Colbert, B., Mohammadi, H. & Peet, M., Aug 9 2018, 2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., Vol. 2018-June. p. 2190-2197 8 p. 8431203

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

Polynomials
Global optimization
1 Citation (Scopus)

Estimating the region of attraction using polynomial optimization: A converse Lyapunov result

Jones, M., Mohammadi, H. & Peet, M., Jan 18 2018, 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., Vol. 2018-January. p. 1796-1802 7 p.

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

Lyapunov functions
Converse
Lyapunov Function
Lyapunov
Polynomials
2 Citations (Scopus)

Solving dynamic programming with supremum terms in the objective and application to optimal battery scheduling for electricity consumers subject to demand charges

Jones, M. & Peet, M., Jan 18 2018, 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., Vol. 2018-January. p. 1323-1329 7 p.

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

Supremum
Electricity
Dynamic programming
Battery
Dynamic Programming
2017
2 Citations (Scopus)

A convex reformulation of the controller synthesis problem for MIMO single-delay systems with implementation in SOS

Peet, M., Jun 29 2017, 2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., p. 5127-5134 8 p. 7963750

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

MIMO systems
Controllers
Convex optimization
Testing
2016
2 Citations (Scopus)

Multi-objective dynamic programming for constrained optimization of non-separable objective functions with application in energy storage

Kamyar, R. & Peet, M., Dec 27 2016, 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., p. 5348-5353 6 p. 7799089

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

Energy Storage
Multiobjective Programming
Nonseparable
Constrained optimization
Constrained Optimization
2 Citations (Scopus)

Optimal state feedback boundary control of parabolic PDEs using SOS polynomials

Gahlawat, A. & Peet, M., Jul 28 2016, 2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., Vol. 2016-July. p. 4350-4355 6 p. 7525606

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

State feedback
Polynomials
Controllers
Lyapunov functions
Mathematical operators
3 Citations (Scopus)

Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels

Gahlawat, A. & Peet, M., Feb 8 2016, Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., Vol. 2016-February. p. 1217-1223 7 p. 7402377

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

Parabolic PDEs
Output Feedback Control
Sum of squares
Feedback control
Observer
2 Citations (Scopus)

Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS

Meyer, E. & Peet, M., Feb 8 2016, Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., Vol. 2016-February. p. 1884-1890 7 p. 7402485

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

Lyapunov methods
Lyapunov Methods
Linear partial differential equation
Parabolic Partial Differential Equations
Partial differential equations
2015
3 Citations (Scopus)

Optimal thermostat programming and optimal electricity rates for customers with demand charges

Kamyar, R. & Peet, M., Jul 28 2015, Proceedings of the American Control Conference. Institute of Electrical and Electronics Engineers Inc., Vol. 2015-July. p. 4529-4535 7 p. 7172042

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

Thermostats
Electricity
Costs
Dynamic programming
Public utilities
2014
12 Citations (Scopus)

LMI parametrization of Lyapunov functions for infinite-dimensional systems: A framework

Peet, M., 2014, Proceedings of the American Control Conference. Institute of Electrical and Electronics Engineers Inc., p. 359-366 8 p. 6859228

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

Lyapunov functions
Mathematical operators
Polynomials
Hilbert spaces
Linear systems
2013
3 Citations (Scopus)

A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems

Murti, C. & Peet, M., 2013, 2013 European Control Conference, ECC 2013. p. 1657-1662 6 p. 6669823

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

Hybrid systems
Polynomials
Lyapunov functions
Asymptotic stability
Dynamical systems
2 Citations (Scopus)

Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems

Kamyar, R. & Peet, M., 2013, Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., p. 5858-5863 6 p. 6760813

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

Large-scale Systems
Decentralized
Nonlinear systems
Stability Analysis
Nonlinear Systems
6 Citations (Scopus)

Full-state feedback of delayed systems using SOS: A new theory of duality

Peet, M., 2013, IFAC Proceedings Volumes (IFAC-PapersOnline). p. 24-29 6 p.

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

State feedback
Controllers
Time delay

Stability analysis of state-dependent delay systems using sum-of-squares

Li, B. & Peet, M., 2013, AIAA Guidance, Navigation, and Control (GNC) Conference.

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

Convex optimization
Derivatives
2012
11 Citations (Scopus)

Bootstrap current optimization in Tokamaks using sum-of-squares polynomials

Gahlawat, A., Witrant, E., Peet, M. & Alamir, M., 2012, Proceedings of the IEEE Conference on Decision and Control. p. 4359-4365 7 p. 6426638

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

Sum of squares
Bootstrap
Polynomials
Shape Constraint
Input Constraints
3 Citations (Scopus)

Decentralized computation for robust stability analysis of large state-space systems using Polya's theorem

Kamyar, R. & Peet, M., 2012, Proceedings of the American Control Conference. p. 5948-5954 7 p. 6315268

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

Cluster computing
Linear matrix inequalities
Parallel algorithms
Scalability
Robust stability
4 Citations (Scopus)

Decentralized computation for robust stability of large-scale systems with parameters on the hypercube

Kamyar, R. & Peet, M. M., 2012, Proceedings of the IEEE Conference on Decision and Control. p. 6259-6264 6 p. 6425907

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

Robust Stability
Large-scale Systems
Hypercube
Decentralized
Large scale systems
1 Citation (Scopus)

Positivity of complete quadratic Lyapunov-Krasovskii functionals in time-delay systems

Gu, K., Zhang, Y. & Peet, M., 2012, Lecture Notes in Control and Information Sciences. Vol. 423. p. 35-47 13 p. (Lecture Notes in Control and Information Sciences; vol. 423).

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

time
2011
1 Citation (Scopus)

Biological circuit models of immune regulatory response: A decentralized control system

Peet, M., Kim, P. & Lee, P. P., 2011, Proceedings of the IEEE Conference on Decision and Control. p. 3020-3025 6 p. 6161395

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

Decentralized control
Decentralized Control
Immune system
Immune System
Control System
6 Citations (Scopus)

Control and verification of the safety-factor profile in Tokamaks using sum-of-squares polynomials

Gahlawat, A., Peet, M. & Witrant, E., 2011, IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. Vol. 18. p. 12556-12561 6 p.

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

Safety factor
Polynomials
Controllers
Magnetic flux
State feedback
8 Citations (Scopus)

Designing observer-based controllers for PDE systems: A heat-conducting rod with point observation and boundary control

Gahlawat, A. & Peet, M., 2011, Proceedings of the IEEE Conference on Decision and Control. p. 6985-6990 6 p. 6161289

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

Boundary Control
Observer
Heat
Controller
Controllers
4 Citations (Scopus)

SOS for sampled-data systems

Seuret, A. & Peet, M., 2011, IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. Vol. 18. p. 1441-1446 6 p.

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

Linear systems
Sampling
2010

Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations

Gu, K., Zhang, Y. & Peet, M., 2010, IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. p. 138-143 6 p.

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

Convergence of numerical methods
Difference equations
Polynomials
Derivatives
12 Citations (Scopus)

A converse sum-of-squares Lyapunov result: An existence proof based on the Picard iteration

Peet, M. & Papachristodoulou, A., 2010, Proceedings of the IEEE Conference on Decision and Control. p. 5949-5954 6 p. 5717536

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

Picard Iteration
Polynomial Vector Fields
Local Stability
Sum of squares
Converse
6 Citations (Scopus)

A parallel-computing solution for optimization of polynomials

Peet, M. & Peet, Y., 2010, Proceedings of the 2010 American Control Conference, ACC 2010. p. 4851-4856 6 p. 5530905

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

Parallel processing systems
Polynomials
Parallel algorithms
Costs
2 Citations (Scopus)

Reducing the computational cost of the Sum-of-Squares stability test for time-delayed systems

Zhang, Y., Peet, M. & Gu, K., 2010, Proceedings of the 2010 American Control Conference, ACC 2010. p. 5018-5023 6 p. 5530749

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

Computational complexity
Difference equations
Costs
Time delay
Feedback
2009
1 Citation (Scopus)

A generalized chain rule and a bound on the continuity of solutions and converse Lyapunov functions

Peet, M., 2009, Proceedings of the IEEE Conference on Decision and Control. p. 3155-3161 7 p. 5400414

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

Chain rule
Lyapunov functions
Converse
Lyapunov Function
Ordinary differential equations
5 Citations (Scopus)

Inverses of positive linear operators and state feedback design for time-delay systems

Peet, M. & Papachristodoulou, A., 2009, IFAC Proceedings Volumes (IFAC-PapersOnline). PART 1 ed. Vol. 8. p. 278-283 6 p.

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

State feedback
Time delay
Controllers
Lyapunov functions
Mathematical operators

SOS for nonlinear delayed models in biology and networking

Papachristodoulou, A. & Peet, M., 2009, Lecture Notes in Control and Information Sciences. Vol. 388. p. 133-143 11 p. (Lecture Notes in Control and Information Sciences; vol. 388).

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

non-linear model
networking
biology
Internet
communication

SOS methods for stability analysis of neutral differential Ssystems

Peet, M., Bonnet, C. & Özbay, H., 2009, Lecture Notes in Control and Information Sciences. Vol. 388. p. 97-107 11 p. (Lecture Notes in Control and Information Sciences; vol. 388).

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

programming
mathematics
2008
1 Citation (Scopus)

Global stability analysis of primal internet congestion control schemes with heterogeneous delays

Papachristodoulou, A. & Peet, M., 2008, IFAC Proceedings Volumes (IFAC-PapersOnline). 1 PART 1 ed. Vol. 17.

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

Congestion control (communication)
Internet
Bandwidth
2 Citations (Scopus)

Polynomial Lyapunov functions for exponential stability of nonlinear systems on bounded regions

Peet, M. & Bliman, P. A. J., 2008, IFAC Proceedings Volumes (IFAC-PapersOnline). 1 PART 1 ed. Vol. 17.

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

Lyapunov functions
Asymptotic stability
Nonlinear systems
Polynomials
Ordinary differential equations
5 Citations (Scopus)

Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions

Peet, M. & Papachristodoulou, A., 2008, Proceedings of the IEEE Conference on Decision and Control. p. 847-852 6 p. 4739245

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

Lyapunov functions
Kernel Function
Lyapunov Function
Polynomials
kernel
2007

Exponentially stable nonlinear systems have polynomial lyapunov functions on bounded regions

Peet, M., 2007, 45th Annual Allerton Conference on Communication, Control, and Computing 2007. University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering, Vol. 2. p. 1074-1081 8 p.

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

Lyapunov functions
Nonlinear systems
Polynomials
Differential equations
Asymptotic stability
2 Citations (Scopus)

Positivity of Kernel functions for systems with communication delay

Peet, M. & Papachristodoulou, A., 2007, Proceedings of the IEEE Conference on Decision and Control. p. 2815-2820 6 p. 4434664

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

Mathematical operators
Time delay
Polynomials
Communication
Composite materials
34 Citations (Scopus)

Stability analysis of linear systems with time-varying delays: Delay uncertainty and quenching

Papachristodoulou, A., Peet, M. & Niculescu, S. I., 2007, Proceedings of the IEEE Conference on Decision and Control. p. 2117-2122 6 p. 4434764

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

Linear systems
Quenching
Polynomials
Decomposition
Uncertainty
2006
28 Citations (Scopus)

On the analysis of systems described by classes of partial differential equations

Papachristodoulou, A. & Peet, M., 2006, Proceedings of the IEEE Conference on Decision and Control. p. 747-752 6 p. 4177885

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

Partial differential equations
Polynomials
Boundary conditions
25 Citations (Scopus)

Positive forms and stability of linear time-delay systems

Peet, M., Papachristodoulou, A. & Lall, S., 2006, Proceedings of the IEEE Conference on Decision and Control. p. 187-193 7 p. 4177975

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

Lyapunov functions
Time delay
Set theory
Cones
Differential equations
2005
26 Citations (Scopus)

Constructing Lyapunov-Krasovskii functionals for linear time delay systems

Papachristodoulou, A., Peet, M. & Lall, S., 2005, Proceedings of the American Control Conference. Vol. 4. p. 2845-2850 6 p.

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

Time delay
Linear matrix inequalities
Polynomials
Decomposition
Uncertainty
2004
1 Citation (Scopus)

On global stability of internet congestion control

Peet, M. & Lall, S., 2004, Proceedings of the IEEE Conference on Decision and Control. Vol. 1. p. 1035-1041 7 p.

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

Congestion control (communication)
Dynamic models
Internet
Asymptotic stability
Linearization