SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1831-1856, January 2021.
We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural, for instance, in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$. This also yields a sufficient condition for exponential stability to a special class of systems of linear time-varying difference-delay equations which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference-delay systems is independent of $p$, thereby proving again in a simpler way some results from [Y. Chitour, G. Mazanti, and M. Sigalotti, Netw. Heterog. Media, 11 (2016), pp. 563--601].

中文翻译：

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电报方程或时滞差分方程的时变网络的充分稳定性条件

SIAM数学分析杂志，第53卷，第2期，第1831-1856页，2021年1月。
我们给出了无损电报方程网络的指数稳定性的充分条件，再加上线性时变边界条件。充分的条件取决于耦合的耗散性，这在例如微波电路的情况下是自然的。关于任何$ L ^ p $-范数，$ 1 \ leq p \ leq \ infty $，指数稳定性。这也为一类特殊的线性时变差分-时滞方程组的指数稳定性提供了充分的条件，该系统是相当明确和易于处理的。证明的一个要素是，这种差分延迟系统的$ L ^ p $指数稳定性独立于$ p $，从而再次以更简单的方式证明了[Y. G. Mazanti的Chitour和Netw的M. Sigalotti。杂种 Media，11（2016），第563--601页。