Matrix Root Clustering: History, Methods and Results


Volha Kushel, Shanghai University


2017.12.05 15:00-16:00


Middle Lecture Room, Math Building


In this talk, we consider the problem of matrix and polynomial root clustering in a region D of the complex plane, which has been widely investigated in the last decades. This problem is also referred to as matrix (polynomial) D-stability. Many properties of system dynamics may be defined via D-stability in a specific region. Here, we give a historical overview of the subject. We mention some problems of system and control theory which lead to the study of D-stability as well as the connected problems of robust D-stability and D-stabilization (known also as D-pole placement or pole assignment problem). The most studied classes of the stability regions, including the classical examples, i.e. the left-hand side of the complex plane and the unit disk, are considered. For studying sophisticated regions, a collection of mappings (e.g. Schwarz–Christoffel transformation) of the complex plane is used. We provide the examples of stability regions having special requirements (e.g. LMI regions). Then we consider a number of results which generalize classical stability theorems.