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

TL;DR

This paper establishes conditions under which large-scale distributed nonlinear systems exhibit exponential incremental input/output-to-state stability, using small-gain theorems and Lyapunov methods.

Contribution

It introduces a novel small-gain condition framework for exponential i-IOSS in distributed systems, with LMI-based criteria for practical verification.

Findings

The overall system is exponentially i-IOSS if each subsystem is and the small-gain condition holds.

Lyapunov characterization provides a different quantitative perspective on stability.

LMI conditions on subsystems and interconnections guarantee exponential i-IOSS.

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.