Determining Asymptotic Stability and Robustness of Networked Systems

Abstract

This paper is motivated by the notion that coupling systems allows for mitigating the failure of individual ones. We present a novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions. The analysis relies on a local analysis; thus, making it computationally implementable. We present an efficient computational method that relies on semidefinite programming. Importantly, for cases where multiple equilibrium points exist, we show how to determine regions around an asymptotically stable equilibrium point that bounds solutions. These regions increase when systems are coupled as we observe when applying the presented analysis framework to a mathematical model of a continuous stirred tank reactor. Importantly, the presented work has implications to other fields as well.