TIME-DELAYED BOUNDARY FEEDBACK STABILIZATION OF THE ISOTHERMAL EULER EQUATIONS WITH FRICTION

被引：35
作者：
Gugat, Martin [1 ]
Dick, Markus [1 ]
机构：
[1] Univ Erlangen Nurnberg, Lehrstuhl Angew Math, D-91058 Erlangen, Germany
来源：
MATHEMATICAL CONTROL AND RELATED FIELDS | 2011年 / 1卷 / 04期
关键词：
Boundary control; conservation law; delay; delay term; Euler equations; feedback with delay; feedback stabilization; friction term; gas network; hyperbolic PDE; L-2-norm; Lyapunov function; Riemann invariants; star-shaped network; time delay;
D O I：
10.3934/mcrf.2011.1.469
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the isothermal Euler equations with friction that model the gas flow through pipes. We present a method of time-delayed boundary feedback stabilization to stabilize the isothermal Euler equations locally around a given stationary subcritical state on a finite time interval. The considered control system is a quasilinear hyperbolic system with a source term. For this system we introduce a Lyapunov function with delay terms and develop time-delayed boundary controls for which the Lyapunov function decays exponentially with time. We present the stabilization method for a single gas pipe and for a star-shaped network of pipes.
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收藏
页码：469 / 491
页数：23
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