Monodromy matrix of a periodic linear system ($N=X(P)X(0{)}^{-1}$)

For $\dot{Y}=K(t)Y$ with coefficient period $P$, the monodromy matrix maps $Y(0)$ to $Y(P)$. Its eigenvalues are the Floquet multipliers. For piecewise constant coefficients it is the time-ordered product of the segment matrix exponentials, with the earliest segment on the right. Its determinant is $\exp ({\int }_0^P\mathrm{tr}K(t)dt)$.