On Schur Diagonal Stability

In this paper, a necessary and sufficient condition which ensures the existence of diagonal solution of the Stein inequality for a $2\times 2$ matrix is given. Then, this result is extended to common diagonal solution of finite number of $2\times 2$ matrices. Schur diagonal stability of segment of matrices is also considered. Furthermore, a sufficient condition is obtained for Schur diagonal stability of $3\times 3$ matrices. Some explanatory examples are presented in the text.