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This paper deals with the linear system x' = A(t)x with A(t) being a 2 x 2 matrix. The anti-diagonal components of A(t) are assumed to be periodic, but the diagonal components are not necessarily periodic. Our concern is to establish sufficient conditions for the zero solution to be attractive. Floquet theory is of no use in solving our problem, because not all components are periodic. Another approach is adopted. Some simple examples are included to illustrate the main result.

Attractivity for two-dimensional linear systems whose anti-diagonal coefficients are periodic