A Sum-of-Squares approach to the Stability and Control of Interconnected Systems using Vector Lyapunov Functions

TL;DR

This paper introduces a scalable sum-of-squares based method for analyzing the stability of large interconnected systems using vector Lyapunov functions, enabling local control design and stability verification.

Contribution

It develops a parallel, subsystem-based SOS approach for stability analysis and control of large-scale interconnected polynomial systems, addressing computational challenges.

Findings

Scalable SOS-based stability analysis for large systems

Subsystem Lyapunov functions enable local stability verification

Locally computable control laws ensure asymptotic stability

Abstract

Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial dynamical systems. But for a real-life large scale dynamical system this method becomes inapplicable because of growing computational burden. In such a case, it is important to develop a subsystem based stability analysis approach which is the focus of the work presented here. A parallel and scalable algorithm is used to infer stability of an interconnected system, with the help of the subsystem Lyapunov functions. Locally computable control laws are proposed to guarantee asymptotic stability under a given disturbance.