Design of Control Laws for Robust Global Stabilization of Multistable State Periodic Systems

This paper continues with the development of the input-to-state stability (ISS)-control Leonov function (CLeF) approach. The definitions of practical ISS and integral ISS (iISS)–CLeFs are refined, and the proposed methodology for control synthesis is improved to simplify the final control law. Then, it is shown that the existence of practical ISS- and iISS–CLeFs is a sufficient condition to guarantee the existence of a controller that endows multistable state periodic systems with the ISS and iISS properties, respectively. Furthermore, a methodology for the design of such a controller is provided via the well-known Sontag's universal formula. Besides, an extension of the main result is presented to connect the ISS–CLeF approach with the standard Leonov function method such that the maximal invariant set of the closed-loop system is compact on a manifold. Finally, the proposed approach is applied to the design of an excitation controller for a synchronous generator, which guarantees global ISS properties for the closed-loop system, unlike the usual local results reported in the literature. The obtained control is also independent of the load angle. The effectiveness of the designed controller is demonstrated in simulations.