Abstract
In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.
| Original language | English |
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| Title of host publication | 2013 American Control Conference, ACC 2013 |
| Pages | 3302-3307 |
| Number of pages | 6 |
| State | Published - Sep 11 2013 |
| Event | 2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013 |
Publication series
| Name | Proceedings of the American Control Conference |
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| ISSN (Print) | 0743-1619 |
Conference
| Conference | 2013 1st American Control Conference, ACC 2013 |
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| Country | United States |
| City | Washington, DC |
| Period | 06/17/13 → 06/19/13 |
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Keywords
- Antidiffusion
- Arbitrary exponential decay rate
- Backstepping
- Linearized Korteweg-de Vries systems
- Semigroup of linear operators
Cite this
Tang, S., & Krstic, M. (2013). Stabilization of linearized Korteweg-de Vries systems with anti-diffusion. In 2013 American Control Conference, ACC 2013 (pp. 3302-3307). [6580341] (Proceedings of the American Control Conference).