Stability check of matrix families: how and why vertex solution for multiple vertex case is different from two vertex case

摘要

This work presents a new insight into the problem of checking the stability of matrix families formed by the convex combination of Hurwitz stable matrices. The paper reviews the necessary and sufficient vertex solution offered by the author for testing the robust stability of this family and highlights the difference between the multiple vertex (i.e. number of vertex matrices being /spl ges/3) case and the two vertex case. New insight is provided not only into this difference between these two cases, but also on the importance of computational awareness in the problem formulation and the resulting differences in the vertex algorithm, thereby clarifying many subtleties surrounding the proposed algorithm and helping to explain why it has been such a difficult task to understand and solve all this time. Examples illustrating the application of the vertex algorithm are given. Finally, some conclusions are drawn along with future research directions.