On the generalized stability of families of polynomials

Necessary and sufficient conditions for stability of parameterized families of complex polynomials are obtained as by-products of the authors´ methodology (1989) for robust stability analysis. This methodology entails the use of the concept of guardian maps. In the general framework, the methodology allows the consideration of generalized stability problems involving nonlinear dependence on more than one parameter. As a particular case, a necessary and sufficient condition for generalized stability of the convex combination of two (complex) polynomials is obtained. Recent work of N.K. Bose (1989) on this problem inspires the construction of the guardian maps. Bose´s results follow as a special case of those presented