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Zbl 1183.76660
Sakthivel, Rathinasamy
Robust stabilization the Korteweg-de Vries-Burgers equation by boundary control. (English)
[J] Nonlinear Dyn. 58, No. 4, 739-744 (2009). ISSN 0924-090X; ISSN 1573-269X/e

Summary: The problem of robust global stabilization by nonlinear boundary feedback control for the Korteweg-de Vries-Burgers equation on the domain [0,1] is considered. The main purpose of this paper is to derive nonlinear robust boundary control laws which make the system robustly globally asymptotically stable in spite of uncertainty in the system parameters. Furthermore, we show that the proposed boundary controllers guarantee $L_{2}$-robust exponential stability, $L_{\infty }$-robust asymptotic stability and boundedness in terms of both $L_{2}$ and $L_{\infty }$.

MSC 2000:: *76B75 Flow control and optimization
76B25 Solitary waves, etc. (inviscid fluids)
93C20 Control systems governed by PDE

Keywords: Korteweg-de Vries-Burgers equation; nonlinear boundary feedback control; robust global stability; spatially dependent scaling

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