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 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization
Fingerprint Dive into the research topics of 'Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS'. Together they form a unique fingerprint.
Cite this
Meyer, E., & Peet, M. (2016). Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS. In Proceedings of the IEEE Conference on Decision and Control (Vol. 2016-February, pp. 1884-1890). [7402485] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402485