Root-loci for periodic linear systems

Abstract

According to the Floquet theory, an nth-order linear periodic (LP) system of the form y/sup n/+/spl alpha//sub n/(t) y/sup n-1/+...+/spl alpha//sub 2/(t)dy(t)/dt+/spl alpha//sub 1/(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.