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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