Incremental finite-step input-to-state stability for network of discrete-time switched systems

This paper investigates incrementally input-to-state stability ( $ \mathrm{\delta } $ δISS) for the interconnection of infinitely many finite-dimensional discrete-time switched subsystems (DtSS), using finite-step Lyapunov functions (FSLF). Unlike many previous investigations, each subsystem in the network may be not necessarily δISS, considering the potential effects of subsystems on each other. The proposed analysis method shows that the size of the truncation of an infinite network does not need to be known. As an application, assuming the subsystems only need to have M-step approximate bisimilarity relations, it is possible to construct approximately bisimilar abstractions, under small-gain type conditions. The effectiveness of the proposed technique is illustrated through an islanded microgrid, consisting of infinitely many subsystems.