In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systemṡ x = A(t)x, A(t + T ) = A(t). As a corollary, the lower and upper bounds for the Floquet characteristic exponents are established. The approach is based on the use of logarithmic norm of the system matrix A(t). Finally we analyze the robustness of the stability property under external disturbance.Index Terms-Linear periodic time-varying system, uniform exponential stability, uniform stability, logarithmic norm.