Finite-time incremental (Q,S,R) -dissipativity and finite-time incremental stability for switched nonlinear systems

This paper examines the finite-time incremental (Q,S,R)-dissipativity and finite-time incremental stability of switching nonlinear systems. First, we introduce the concept of finite-time incremental (Q,S,R)-dissipativity, which requires each active subsystem to be finite-time incremental (Q,S,R)-dissipative during its active period and allows the incremental storage function to increase at switching times. Second, by using state information, we design a switching law to achieve finite-time incremental (Q,S,R)-dissipativity, generalising the ‘min’ switching law. Third, multiple-incremental storage functions method is employed to obtain the finite-time incremental stability, even if none of the subsystems are finite-time incrementally (Q,S,R)-dissipative. Finally, to validate our findings, two examples are provided.