Small-Gain Theorem for Safety Verification of Interconnected Systems

TL;DR

This paper develops a small-gain theorem using barrier functions to verify safety in interconnected systems, enabling safety analysis of complex systems from subsystem information.

Contribution

It introduces a novel small-gain theorem formulation for barrier functions, facilitating safety verification of interconnected systems and higher-dimensional safety set construction.

Findings

Enables safety verification of interconnected systems using ISSf-barrier functions

Allows construction of higher-dimensional safety sets from lower-dimensional ones

Provides a method to verify input-to-state safety in complex systems

Abstract

A small-gain theorem in the formulation of barrier function is developed in this work for safety verification of interconnected systems. This result is helpful to verify input-to-state safety (ISSf) of the overall system from the safety information encoded in the subsystem's ISSf-barrier function. Also, it can be used to obtain a safety set in a higher dimensional space from the safety sets in two lower dimensional spaces.