A note on uniform exponential stability of linear periodic time-varying systems

Abstract

In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ 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.