Finite Nyquist and Finite Inclusions Theorems for disjoint stability regions

Finite Nyquist Theorem is an important tool in stability analysis and design of linear systems. Currently, Finite Nyquist Theorem can treat only simply connected convex stability regions with some extensions to simply connected non-convex regions. In this paper, we consider the generalization of Finite Nyquist Theorem for the case of union of disjoint convex stability regions. Based on this result, the Finite Inclusions Theorem is also formulated for a union of disjoint convex stability regions.