Controllability and (ir-)reducibility of Floquet factorizations in continuous-time periodic systems

The paper examines reducibility/irreducibility of Flouqet factorizations and explicates their relationship with controllability in finite-dimensional linear continuous-time periodic (FDLCP) systems. Reducibility/irreducibility of Floquet factorizations reflect numeric aspects of the transition matrix representation in FDLCP systems that can be attributed to matrix logarithm, which remain unnoticed mostly so far in the Floquet theory. Controllability criteria are claimed by means of Floquet factorizations, including a harmonic PBH test. The results reveal that Floquet factorizations may distort or alter controllability structure when unequally reducible Floquet factors are used separately. Numeric examples are included.