Strong and Weak Leonov Functions for Global Boundedness of State Periodic Systems

We present new results for the analysis of global boundedness of state periodic systems. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a
part
of the state vector, and the case of systems, whose dynamics is periodic with respect to
all
state variables. To derive the results, the notion of
strong
Leonov functions is introduced. The main results are complemented by a number of relaxations based on the concept of
weak
Leonov functions.