A case study of frozen-time eigenvalues in the stability analysis for periodic linear systems

The stability of linear time-varying systems can be assessed using frozen-time eigenvalues (system eigenvalues computed at each instant). The failure of the sufficiency part of this method was illustrated by L. Markus and M. Yamabe (1960). Their example is examined in a more general setting and in the light of the Floquet characteristic exponent theory which leads to some interesting and enlightening results. These results provide deeper insight into and better understanding of the concept of frozen-time eigenvalues and Floquet characteristic exponents. They are also useful in the robustness analysis for linear time-invariant systems, since the nominal eigenvalues in that case are the frozen-time eigenvalues of the perturbed systems used in such analysis