Common Solutions to Stein Inequalities

Authors : Şerife Yilmaz, Birgül Aksoy

Pages : 1097-1103

Doi:10.16984/saufenbilder.1260438

View : 85 | Download : 105

Publication Date : 2023-10-18

Article Type : Research Paper

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