Stability verification of multidimensional Kirchoff circuits by suitable energy functions

Multidimensional (MD) Kirchoff circuits (MDKC) are introduced in the theory of MD wave digital filters (MDWDF) in order to develop the so-called reference networks. Since MDWDF principles have also been used for numerical integration of partial differential equations (PDE) having physical relevance, MDKCs have received new significance because they can be used as an equivalent alternative representation of the original PDEs. For this reason it has become interesting to develop a more complete theory of MDKCs. A new energy function is represented to serve as a possible stability criterion for the MDKCs in the sense of Lyapunov (1966)