On Two Problems for Matrix Polytopes

Şerife Yılmaz, Taner Büyükköroğlu

Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey.

DOI: 10.4236/am.2014.517253                

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.

Keywords

Stable Matrix, Matrix Family, Common Quadratic Lyapunov Functions, Switched System, Gradient Method

Conflicts of Interest

The authors declare no conflicts of interest.

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