Some new results in linear time-varying systems

This correspondence presents some new results for linear time-varying systems
\dot{x}(t)=A(t)x(t)
. These new results include, 1) an explicit necessary and sufficient condition of stability that can be determined directly by joint eigenvalues of two constant matrices, and 2) a new class of reducible systems which needs not be periodic, as is required in Floquet theory.