Open AccessOn Cauchy´s Interlacing Theorem and the Stability of an Aggregation -type Epidemic Model
Author(s) -
Manuel De la Sen
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/790/1/012090
Subject(s) - interlacing , hermitian matrix , matrix similarity , cauchy distribution , mathematics , transformation matrix , formalism (music) , discrete time and continuous time , control theory (sociology) , computer science , pure mathematics , mathematical analysis , control (management) , partial differential equation , artificial intelligence , art , musical , statistics , physics , kinematics , classical mechanics , visual arts , operating system
Some convergence results are applied to a dynamic discrete system which is built by aggregation of discrete dynamic subsystems subject to linear output feedback control. Since we are dealing with physical systems, it turns out that the formalism can be developed by invoking conditions related to real symmetric systems rather than to complex Hermitian ones when necessary. It would suffice to describe the state by expressing the matrix of dynamics in the real canonical form and to transform accordingly the control and output matrices by the appropriate similarity transformation. The results are shown to be of usefulness for the analysis of discrete aggregation- type epidemic models.