Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices |
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Authors: | M Medved’ M Pospíšil |
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Institution: | 1. Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia;2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia |
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Abstract: | In this paper a generalization of the delayed exponential defined by Khusainov and Shuklin (2003) 1] for autonomous linear delay systems with one delay defined by permutable matrices is given for delay systems with multiple delays and pairwise permutable matrices. Using this multidelay-exponential a solution of a Cauchy initial value problem is represented. By an application of this representation and using Pinto’s integral inequality an asymptotic stability results for some classes of nonlinear multidelay differential equations are proved. |
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Keywords: | 34A34 34D20 34K27 |
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