Incremental (Q,S,R)-dissipativity and incremental stability for switched nonlinear systems

This paper investigates incremental (Q,S,R)-dissipativity and incremental stability for switched nonlinear systems whose subsystems are not required to be incrementally (Q,S,R)-dissipative. Firstly, an incremental (Q,S,R)-dissipativity concept is proposed for switched nonlinear systems. We show that an incrementally (Q,S,R)-dissipative switched nonlinear system is incrementally stable. Secondly, the sufficient conditions for switched nonlinear systems to be incrementally (Q,S,R)-dissipative are given by the design of state-dependent switching laws. Finally, this incremental (Q,S,R)-dissipativity property is shown to be invariant under compatible feedback interconnection by the design of a composite state-dependent switching law. The numeral examples are presented to illustrate the effectiveness of the proposed approach.