Small-gain analysis of exponential incremental input/output-to-state stability for large-scale distributed systems

Abstract: We provide a detectability analysis for nonlinear large-scale distributed systems in the sense of exponential incremental input/output-to-state stability (i-IOSS). In particular, we prove that the overall system is exponentially i-IOSS if each subsystem is i-IOSS, with interconnections treated as external inputs, and a suitable small-gain condition holds. The analysis is extended to a Lyapunov characterization, resulting in a different quantitative outcome regarding the small-gain condition, which is further analyzed within this work. Moreover, we derive linear matrix inequality conditions posed solely on the local subsystems and their interconnections, which guarantee exponential i-IOSS of the overall distributed system. The results are illustrated on a numerical example.