Necessary and sufficient conditions for robust stability of a continuous system-the continuous dependency case illustrated via multilinear dependency

It is noted that problems of testing robust stability of linear systems with structured uncertainty are formulated, from the mathematical viewpoint, as methods for testing the nonvanishing of a polynomial whose coefficients are functions of interval (uncertain) parameters, in a certain domain in the complex plane. In the present work, a recently derived theorem is reformulated (with new direct proof) to be pertinent in particular to such problems, where the domain is the closed right-half complex plane. Applying this reformulated theorem to the two-parameter multilinear dependency case, the author obtains explicit necessary and sufficient conditions.>