- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Cilt: 27 Sayı: 5
- Common Solutions to Stein Inequalities
Common Solutions to Stein Inequalities
Authors : Şerife Yilmaz, Birgül Aksoy
Pages : 1097-1103
Doi:10.16984/saufenbilder.1260438
View : 70 | Download : 96
Publication Date : 2023-10-18
Article Type : Research
Abstract :In this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence of a common solution of Stein equation are given. As in the case of continuous time systems, the problem of existence of a common solution is reduced to a convex optimization one. An efficient solution algorithm which requires solving a linear minimax problem at each step is suggested. The algorithm is supported with a number of examples from the literature and observed that the method desired results fastly.Keywords : Discrete-time system, Schur stability, Stein equation, common quadratic Lyapunov function, Schur complement