Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations

Abstract

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, $1\le p\le \infty$. This also yields a sufficient condition for exponential stability to a special class of linear time-varying difference delay systems 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 reproving in a simpler way some results from [Y. Chitour, G. Mazanti, and M. Sigalotti, $Netw.Heterog.Media$, 11 (2016), pp. 563--601].

To be published in SIAM Journal on Mathematical Analysis, most probably 2021

Cited by in corpus (3)

• Left-coprimeness condition for the reachability in finite time of pseudo-rational systems of order zero with an application to difference delay systems
• Integral representation formula for linear non-autonomous difference-delay equations
• Exponential stability of linear periodic difference-delay equations