Passivity-based stabilization for a strict-feedback nonlinear system under a proper state-dependent switching

In this paper, the passivity-based stabilization problem of a strict-feedback nonlinear system under a proper state-dependent switching law is investigated. Here, the feedback passification problem of each subsystem does not need to be solvable. First, by using the recursive backstepping technique, a sufficient condition under which the closed-loop switched system with designed state feedback controllers is strictly passive from the new input to a designed virtual output is given under a state-dependent switching law. Moreover, the asymptotical stability property of the switched system is achieved by redesigning the introduced new input based on passivity. Finally, a numeral example shows the effectiveness of the proposed method.