Abstract
In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and their time derivatives by polynomials and express stability as optimization over polynomials. We use Sum-of-Squares and Positivstellensatz results to numerically search for a solution to the optimization over polynomials. We also show that our algorithm can be used to estimate the rate of decay of the solution to PDE in the L2 norm. Finally, we validate the technique by applying our conditions to the 2D biological KISS PDE model of population growth and an additional example.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the IEEE Conference on Decision and Control |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 1884-1890 |
| Number of pages | 7 |
| Volume | 2016-February |
| ISBN (Print) | 9781479978861 |
| DOIs | |
| State | Published - Feb 8 2016 |
| Event | 54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015 |
Other
| Other | 54th IEEE Conference on Decision and Control, CDC 2015 |
|---|---|
| Country | Japan |
| City | Osaka |
| Period | 12/15/15 → 12/18/15 |
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ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Cite this
Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS. / Meyer, Evgeny; Peet, Matthew.
Proceedings of the IEEE Conference on Decision and Control. Vol. 2016-February Institute of Electrical and Electronics Engineers Inc., 2016. p. 1884-1890 7402485.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS
AU - Meyer, Evgeny
AU - Peet, Matthew
PY - 2016/2/8
Y1 - 2016/2/8
N2 - In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and their time derivatives by polynomials and express stability as optimization over polynomials. We use Sum-of-Squares and Positivstellensatz results to numerically search for a solution to the optimization over polynomials. We also show that our algorithm can be used to estimate the rate of decay of the solution to PDE in the L2 norm. Finally, we validate the technique by applying our conditions to the 2D biological KISS PDE model of population growth and an additional example.
AB - In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and their time derivatives by polynomials and express stability as optimization over polynomials. We use Sum-of-Squares and Positivstellensatz results to numerically search for a solution to the optimization over polynomials. We also show that our algorithm can be used to estimate the rate of decay of the solution to PDE in the L2 norm. Finally, we validate the technique by applying our conditions to the 2D biological KISS PDE model of population growth and an additional example.
UR - http://www.scopus.com/inward/record.url?scp=84962013836&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84962013836&partnerID=8YFLogxK
U2 - 10.1109/CDC.2015.7402485
DO - 10.1109/CDC.2015.7402485
M3 - Conference contribution
AN - SCOPUS:84962013836
SN - 9781479978861
VL - 2016-February
SP - 1884
EP - 1890
BT - Proceedings of the IEEE Conference on Decision and Control
PB - Institute of Electrical and Electronics Engineers Inc.
ER -