New Stability and Exact Observability Conditions for Semilinear Wave Equations
New Stability and Exact Observability Conditions for Semilinear Wave Equations
复制标题
半线性波动方程新的稳定性和精确可观测性条件
DOI：
10.1016/j.automatica.2015.10.008
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Maria Terushkin
中科院分区：
文献类型：
--
作者：
E. Fridman;Maria Terushkin
利用前向和后向观测器序列，通过线性矩阵不等式(LMI)推导出精确可观测时间的上界，解决了有限区间上具有全局Lipschitz非线性的一维波动方程的初始状态估计问题(Fridman，2013)。在本文中，我们将这一结果推广到超立方体上的n维波动方程。这一推广包括了新的基于LMI的n维波动方程的指数稳定性条件，以及关于LMI的最小精确可观测时间的一个上界。对于具有局部Lipschitz非线性的一维波动方程，我们在保证从测量中唯一恢复的初始条件的区域上找到了一个估计。数值算例说明了结果的有效性。
The problem of estimating the initial state of 1-D wave equations with globally Lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers, and deriving the upper bound for exact observability time in terms of Linear Matrix Inequalities (LMIs) (Fridman, 2013). In the present paper, we generalize this result to n-D wave equations on a hypercube. This extension includes new LMI-based exponential stability conditions for n-D wave equations, as well as an upper bound on the minimum exact observability time in terms of LMIs. For 1-D wave equations with locally Lipschitz nonlinearities, we find an estimate on the region of initial conditions that are guaranteed to be uniquely recovered from the measurements. The efficiency of the results is illustrated by numerical examples.