Exponential stability of a coupled Heat-ODE system
Exponential stability of a coupled Heat-ODE system
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DOI：
10.1109/ccdc.2013.6560914
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Dong‐xia Zhao;Jun‐min Wang
中科院分区：
文献类型：
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作者：
Dong‐xia Zhao;Jun‐min Wang
本文研究了一类具有Dirichlet互连的互连系统的反馈镇定问题。热方程与常微分方程组之间的“互联”是双向的，热方程的狄里克莱特边界观测值被送入常微分方程组，常微分方程组的速度则流入热方程的边界。研究中采用了半群方法。通过详细的分析，我们得到了特征值和特征函数的渐近表达式。证明了存在一个广义本征函数序列，它构成了Hilbert状态空间的Riesz基。由此推导出C0半群的谱决定增长条件，并由此得到系统的指数稳定性。给出了数值模拟结果。
This paper addresses the feedback stabilization of an interconnected Heat-ODE system with the Dirichlet interconnection. The “interconnection” between the heat equation and the ODE are bi-directional, in which the Dirichlet boundary observation of the heat equation is fed into the ODE, and the velocity of ODE is flowed into the boundary of the heat equation. The semigroup approach is adopted in investigation. By a detailed analysis, we obtain the asymptotic expressions of eigenvalues and eigenfunctions. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the C0-semigroup, and as a consequence, the exponential stability of the system is then followed. Numerical simulations are presented.