ISS and integral-ISS of switched systems with nonlinear supply functions

The problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results.

Automated summary

This paper investigates the input-to-state stability (ISS) and integral version (iISS) of switched nonlinear systems with inputs, resets, and possibly unstable subsystems. By utilizing dissipation inequalities, supply functions, and the change in Lyapunov functions at switching instants, a formula relating average dwell-time (ADT) and average activation time (AAT) is derived to ensure the stability of the switched system. Case studies are included to illustrate the results.