Analysis of nonautonomous systems of ordinary differential equations with exponentially periodic matrix

We investigate a class of nonautonomous systems of ordinary differential equations whose matrix can be characterized as exponentially periodic. We develop the algorithm of spectral analysis of these systems. By this algorithm we prove reducibility theorems. The proposed algorithm is based on the splitting method that allows to reduce considered systems to simpler ones with quasidiagonal matrix, and formulate constructive conditions of solutions stability.