This paper presents a new methodology for the transient analysis of nanointerconnects, modeled as lossy and dispersive multiconductor transmission lines. The proposed model is derived from the solution of the Telegrapher's equations in the framework of the Sturm-Liouville theory. The open-ended impedance matrix is expressed in a series form as a sum of infinite rational functions, derived by the series form of the Green's function. Hence, a pole-residue rational model can be synthesized and a reduced-order model to be generated by a simple selection of dominant poles. The spectral form of the Green's function also allows to generate a rational model for the transient voltage sensitivity as well. The numerical results confirm the robustness of the proposed technique and its suitability to be adopted in the design flow of next generation nanointerconnects for signal integrity and electromagnetic compatibility purposes.