Periodic Linear Systems

when A is a continuous periodic n× n matrix function of t; i.e., when there is a constant T > 0 such that A(t + T ) = A(t) for every t ∈ R. When that condition is satisfied, we say, more precisely, that A is T -periodic. If T is the smallest positive number for which this condition holds, we say that T is the minimal period of A. Let A be T -periodic, and let X(t) be a fundamental matrix for (1). Define X̃ : R → L(R ,R) by X̃(t) = X(t + T ). Clearly, the columns of X̃ are linearly independent functions of t. Also,