Simple stability criterion for quasipolynomial families with uncertain coefficients and uncertain delays

In this note we consider a robust stability problem for a family of complex-coefficient diamond quasipolynomials. It is shown that the entire quasipolynomial family is stable if and only if eight two-parameter quasipolynomial families are stable, in addition to a simple arithmetical condition. An efficient stability criterion for a two parameter quasipolynomial family is now being investigated. The simplicity of the stability test is achieved on account of special restrictions imposed on coefficients of the quasipolynomial family. Analogous technique may be applied to real diamond or box quasipolynomials with uncertain delays. For these problems the number of two parameter quasipolynomial families that should be checked for stability may depend on the number of delays