A New Method for Evaluating Floquet Characteristic Exponents of Periodic Linear Systems

It is well-known that the stability of linear periodic (LP) systems can be assessed using Floquet Characteristic Exponents (FCE). In this paper, a new method is presented for evaluating FCE for nth-order scalar periodic linear systems based on a recently developed unified eigenvalue theory for linear time-varying (LTV) Systems [1]. The new theory allows FCEs to be evaluated from the DC term of the Fourier series of periodic PD-eigen-values of a LP system. Comparing to the well-known Monodromy Matrix (MM) method and Infinite Dimensional Determinant (IDD) method for evaluating FCE1 the solutions obtained by the new method have rapid local convergence. This new method also allow stability boundaries in the parameter space of a LP system to be evaluated and plotted directly. The new results shed some light OL the general stability assessment problem for vector periodic linear systems and aperiodic LTV systems. Further studies along this direction are also discussed in this paper.