Partial Reluctance K Based Circuit Analysis Is Stable

ABSTRACT Although the stability of ir uit analysis based on partial relu tan e K has been proved for parallel bus stru tures [5℄ and the stru tures with suÆ iently dis retized ondu tors [4℄, the stability for general inter onne t topologies has not been proved. This paper proved that full partial relu tan e matrix and sparsi ed partial relu tan e matrix obtained by ignoring small mutual terms in partial relu tan e extra tion is positive de nite for any inter onne t stru tures, whi h is the ne essary and suÆ ient ondition for the ir uit analysis based on partial relu tan e to be stable.