STARS OF VIBRATING STRINGS: SWITCHING BOUNDARY FEEDBACK STABILIZATION

被引:27
作者
Gugat, Martin [1 ]
Sigalotti, Mario [2 ]
机构
[1] Lehrstuhl 2 Angew Math, D-91058 Erlangen, Germany
[2] Inst Elie Cartan Nancy Math, Projet CORIDA, Ctr Rech Nancy Grand Est, INRIA, F-54506 Vandoeuvre Les Nancy, France
关键词
hyperbolic pde; network; feedback stabilization of pdes; switching control; wave equation; switching feedback; robustness; SYSTEMS;
D O I
10.3934/nhm.2010.5.299
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider a star-shaped network consisting of a single node with N >= 3 connected arcs. The dynamics on each arc is governed by the wave equation. The arcs are coupled at the node and each arc is controlled at the other end. Without assumptions on the lengths of the arcs, we show that if the feedback control is active at all exterior ends, the system velocity vanishes in finite time. In order to achieve exponential decay to zero of the system velocity, it is not necessary that the system is controlled at all N exterior ends, but stabilization is still possible if, from time to time, one of the feedback controllers breaks down. We give sufficient conditions that guarantee that such a switching feedback stabilization where not all controls are necessarily active at each time is successful.
引用
收藏
页码:299 / 314
页数:16
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