The stability of linear periodic Hamiltonian systems on time scales

In this work, we give a new stability criterion for planar periodic Hamiltonian systems, improving the results from the literature. The method is based on an application of the Floquet theory recently established in [J.J. DaCunha, J.M. Davis, A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems, J. Differential Equations 251 (2011) 2987–3027], and the use of a new definition for a generalized zero. The results obtained not only unify the related continuous and discrete ones but also provide sharper stability criteria for the discrete case.