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Influence of anti-diagonals on the asymptotic stability for linear differential systems

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Abstract

Sufficient conditions are given for asymptotic stability of the linear differential system x′  =  B(t)x with B(t) being a 2  ×  2 matrix. All components of B(t) are not assumed to be positive. The matrix B(t) is naturally divisible into a diagonal matrix D(t) and an anti-diagonal matrix A(t). Our concern is to clarify a positive effect of the anti-diagonal part A(t)x on the asymptotic stability for the system x′  =  B(t)x.

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  1. Department of Mathematics and Computer Science, Shimane University, Matsue, 690-8504, Japan

    Jitsuro Sugie

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  1. Jitsuro Sugie
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Correspondence to Jitsuro Sugie.

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Communicated by A. Jüngel.

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Sugie, J. Influence of anti-diagonals on the asymptotic stability for linear differential systems. Monatsh Math 157, 163–176 (2009). https://doi.org/10.1007/s00605-008-0030-x

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  • DOI: https://doi.org/10.1007/s00605-008-0030-x

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