On series connection of infinitely many RLC two-ports. (English) Zbl 1338.93044
Summary: In this paper we study the asymptotic behaviour of infinite systems of first- and second-order linear differential equations arising from the series connection of infinitely many identical \(RLC\) two-ports. These systems exhibit nearest-neighbour dynamics that arise in many aspects of classical and modern physics. We study both the “no capacitor” case, which is a first-order system, and the second-order systems that correspond to damped and undamped oscillators.
MSC:
| 93A15 | Large-scale systems |
| 93C05 | Linear systems in control theory |
| 34D20 | Stability of solutions to ordinary differential equations |
Keywords:
asymptotic behaviour; \(RLC\) two ports; semigroups of operators; strong stability of linear infinite-dimensional systemsReferences:
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