Robust multivariate interval strictly positive functions

Strictly positive (SP) (strictly positive real (SPR)) rational functions form foundations in network realizability theory. Study of boundary implications for the SP (SPR) property of interval rational functions is therefore meaningful. It is proved that the SP (SPR) property of a set of complex (real) N-variable interval rational functions can be implied by the SP (SPR) of its specific 16(2") (16(2^n-1)) extreme members. It is also proved that the positive rational (PR) property of a set of complex univariate interval rational functions can be guaranteed by the PR of its certain 32 extreme members