UNIFORM STABILIZATION OF 1-D COUPLED WAVE EQUATIONS WITH ANTI-DAMPINGS AND JOINT DELAYED CONTROL

摘要

In this paper, we consider the uniform stabilization problem for a coupled 1-d variable coefficient wave equation with anti-dampings in the interior domain and joint difference-type control. We use the integral-type feedback control to stabilize the system, in which the integral kernel functions are regarded as parameters. Our goal in the present paper is to select appropriate kernel functions such that the closed-loop system is exponentially stable. We first choose an exponentially stable system as a target system. Meanwhile, we introduce an appropriate auxiliary system. After that we construct two transformations. The first one is used to establish the equivalence between the original controlled time-delay system and the auxiliary system. This step mainly removes the effect of input memory. The second one is used to establish the equivalence between the auxiliary system and the stable target system. This step is to eliminate the negative effect of the anti-damping. Herein we mainly give an approach to selecting parameter functions in both transformations and hence get an exponentially stable-type feedback controller. Finally, some simulations are used to show the effectiveness of the proposed controller.