Regional passivity for switched nonlinear systems and its application

A framework of regional passivity theory for switched systems is set up using multiple barrier storage functions. The "energy" stored in each subsystem is described by the corresponding individual barrier storage function which is only well defined on an open region associated with regional passivity. The key feature is that the "energy" grows to infinity when the trajectory tends to the region boundary. Firstly, a sufficient condition guaranteeing regional passivity for a switched system is derived under the designed switching law, where all subsystems are not assumed to be regionally passive. Secondly, asymptotic stability can be reached if a switched system is strictly regionally passive or regionally passive plus asymptotic detectability, and meanwhile the system trajectory remains in the corresponding open region. Thirdly, regional passivity is also shown to be preserved under feedback interconnection. Finally, as an application of the theory provided, the stabilization problem for state-constrained strict-feedback switched nonlinear systems is solved, where no subsystem is required to be stabilizable.