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On Two Problems for Matrix Polytopes
Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey
Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey
- 1 Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey
- 2 Department of Mathematics, Faculty of Science, Anadolu University, Eskisehir, Turkey
Applied Mathematics·Volume 05 (2014)·Pages 2650–2656·Published 9 October 2014·DOI10.4236/am.2014.517253
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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.
KeywordsStable MatrixMatrix FamilyCommon Quadratic Lyapunov FunctionsSwitched SystemGradient Method
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