A new approach to construct and extend the Schur stable matrix families

Abstract

In this study, Schur stability, sensitivity and continuity theorems have been mentioned. In addition, matrix families, interval matrix and extend of the intervals also have been mentioned. The $\mathcal{I}_{\mathcal{L}}$ and $\mathcal{I}_{\mathcal{C}}$ iintervals of the matrix families have been determined so that the linear sums family $\mathcal{L}$ and convex combination family $\mathcal{C}$ are Schur stable. Samely, the $\mathcal{I}^{*}_{\mathcal{L}}$ and $\mathcal{I}_{\mathcal{C}}^{\ast }$ intervals have been determined and $\mathcal{L}$ and $\mathcal{C}$ are $\omega ^{\ast }-$Schur stable. Afterwards, the methods which based on continuity theorems and the algorithms which based on the methods have been given. Extended intervals have been obtained with the help of the methods and the algorithms. All definitions are supported by examples.