Abstract
This paper deals with the linear systemx′=A(t)x\mathbf {x}’ = A(t)\mathbf {x}withA(t)A(t)being a2×22\times 2matrix. The anti-diagonal components ofA(t)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.
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