Design of Controls for Boundedness of Trajectories of Multistable State Periodic Systems

In this paper, the concept of control Leonov functions is introduced, and it is shown that their information is enough to design continuous and periodic controllers that provide boundedness of the state for a class of multistable state-periodic systems. These feedback control laws are based on a mild adaptation of Sontag's universal formula, and a kind of small control property. The proposed method is illustrated via application in a microgrid.