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.
Discretetime system, Schur stability, Stein equation, common quadratic Lyapunov function, Schur complement
Primary Language  English 

Subjects  Mathematical Sciences 
Journal Section  Research Articles 
Authors 

Early Pub Date  October 5, 2023 
Publication Date  October 18, 2023 
Submission Date  March 5, 2023 
Acceptance Date  July 25, 2023 
Published in Issue  Year 2023 Volume: 27 Issue: 5 
Sakarya University Journal of Science (SAUJS)