On stability regions of affine matrix families

In this thesis, the location of the set of eigenvalues of the family of affine matrices in the complex plane has been investigated. The location of the matrix eigenvalues in the complex plane characterizes the asymptotic stability of the system determined by that matrix. In the stability problem of affine polynomial families, the Edge Theorem guarantees the robust stability of that family. In affine matrices family, on the other hand, the robust stability of the family cannot be guaranteed from the stability of its edges. In this study, a matrix family for which the edge theorem is valid for affine matrices family is discussed. The stability of the family of affine matrices is equivalent to the stability of the characteristic polynomials of these matrices. In a special case, the characteristic polynomial family can be obtained multilinearly. An example of such matrix families is given. Given the family of affine matrices, the problem of finding a Q box in which this set is robustly stable is addressed. Explanatory examples are given for applications related to the problems discussed.