Stability analysis of periodic linear dynamical systems using a new time-varying eigenvalue concept

The relation between the classical G. Floquet characteristic exponents (1879) and entities called ED (essential D) eigenvalues and PED (primary essential D) eigenvalues for specified scalar periodic linear systems is established. In particular, some important results on the existence and uniqueness of periodic ED-eigenvalues and periodic PED-eigenvalues for these systems are obtained, and it is shown that the mean value of periodic PED-eigenvalues for these systems are their classical Floquet characteristic exponents. Using these results, the authors derive two necessary and sufficient stability criteria for F-nonderogatory and F-derogatory scalar periodic linear systems. The derived stability criteria not only serve to unify the stability theory for the general scalar time-varying linear system, but can also be used to develop novel techniques for evaluating and/or approximating the Floquet characteristic exponents for scalar periodic linear systems