Root-loci for periodic linear systems

According to the Floquet theory, an nth-order linear periodic (LP) system of the form yⁿ+α_n (t) y^n-1+...+α₂(t)dy( t)/dt+α₁(t)y=0 can be transformed into an equivalent linear time-invariant (LTI) system whose characteristic roots, known as Floquet characteristic exponents (FCEs), determine the stability of the LP system. A technique for obtaining an approximation of the characteristic equation for the FCEs is developed. Parametric loci of the FCE, similar to the root locus plot for a LTI system, are then developed for the LP system. The technique is exemplified by 2nd-order LP systems. The FCE loci are useful in the stability analysis and control design for LP systems