TITLE:
On Two Problems for Matrix Polytopes
AUTHORS:
Şerife Yılmaz, Taner Büyükköroğlu
KEYWORDS:
Stable Matrix, Matrix Family, Common Quadratic Lyapunov Functions, Switched System, Gradient Method
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.17,
October
9,
2014
ABSTRACT: We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and give a new sufficient condition for the second problem. A number of examples are considered.