Generation of limit cycles in hybrid systems consisting of two linear subsystems

This paper investigates how a set of full-state feedback controllers can be coupled to a linear system through a hybrid switching scheme to produce limit cycles with desired amplitude and frequency. To this point there has been no investigation of how to apply hybrid control to design limit cycles with desired bulk properties (amplitude and frequency) in otherwise linear systems obeying kinematic constraints. This is an important topic because the ability to synthesize and tune limit cycles provides a means for implementing self-stabilizing periodic patterns of motion in dynamic systems.