Hybrid control design for limit cycle stabilisation of planar switched systems
Résumé
This paper addresses the control problem of an important class of hybrid dynamical systems where the desired state does not belong to the set of subsystem equilibria. Beyond the practical stabilisation where the system trajectory has to be driven to a neighbourhood of a desired state, a control law is designed to solve the limit cycle stabilisation problem for planar hybrid systems. Using the hybrid Poincaré map, two hybrid controllers are developed, which guarantee a local asymptotic/finite-time stability of the desired limit cycle. Illustrative examples are provided to highlight the effectiveness of the derived results.