Stability of a diamond-type quasipolynomial family

Both delay independent and delay-dependent robust stability conditions for a special quasipolynomial family are obtained. We associate with the quasipolynomial family a multivariate polynomial family with a composed diamond structure. This structure allows to obtain vertex type stability results for the polynomial family, which imply delay independent stability conditions for the original quasipolynomial family. Additionally, necessary and sufficient delay dependent stability conditions are also derived.