Feedback boundary control of linear hyperbolic equations with stiff source term
Feedback boundary control of linear hyperbolic equations with stiff source term
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DOI：
10.1080/00207179.2016.1276635
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发表时间：
2018-01
影响因子：
2.1
通讯作者：
M. Herty;Hui Yu
中科院分区：
文献类型：
--
作者：
M. Herty;Hui Yu
摘要考虑具有刚性源项的双曲型系统的反馈边界控制。通过结合加权李雅普诺夫函数，该结构用于推导稳定结果。在我们的分析中，我们给出了稳定的反馈法，允许一个强大的统一指数稳定的一个不确定的参数与衰减率是独立的参数的值的整个范围。特别是，我们感兴趣的极限情况下，当松弛参数接近零。结果示出的数值分析的李雅普诺夫函数的衰减率的刚性参数和应用程序的管道中的气体动力学的边界稳定。
ABSTRACT We consider feedback boundary control of hyperbolic systems with stiff source terms. By combining weighted Lyapunov functions, the structure is used to derive stabilisation results. In our analysis, we give stabilising feedback laws that allow a robust uniform exponential stabilisation for a whole range of values of an uncertain parameter with a decay rate that is independent of the parameter. In particular, we are interested in the limit case when the relaxation parameter approaches zero. The result is illustrated with the numerical analysis on the decay rate of the Lyapunov function in terms of the stiff parameter and an application to boundary stabilisation of gas dynamics in pipes.