Global Asymptotic Stability for General Linear MIMO Distributed Systems: An Approach Based on Robust-Adaptive Controllers

TL;DR

This paper develops a scalable distributed control approach using robust-adaptive controllers and Lyapunov functions to ensure global asymptotic stability in linear MIMO systems with large-gain interconnections, validated on power networks.

Contribution

It extends collective stability methods to adaptive controllers and introduces a systematic approach using Lyapunov functions and Riccati equations for stability assurance.

Findings

The proposed method guarantees stability in large-gain interconnection systems.

Distributed controllers require only local and neighboring subsystem information.

Validation on a DC power network demonstrates effectiveness.

Abstract

Stability is a critical feature of distributed linear multi-input-multi-output systems. Global asymptotic stability usually can be guaranteed when using decentralised or distributed control architectures, if: (i) conservative controllers are designed, (ii) collective stability conditions are satisfied, or (iii) interaction terms are neutral. This paper extends the collective stability method to incorporate adaptive controllers, and shows that this method is insufficient for systems with large-gain interconnections. Subsequently, we show that global asymptotic stability can be systematically ensured by exploiting vector Lyapunov functions and algebraic Riccati equations. This leads to a scalable distributed architecture where local controllers require information from corresponding subsystems and neighbouring controllers. Conveniently, the communication flow has the same topology as the interconnection graph. Theoretical results are validated through application of the proposed architecture to voltage control of a DC power network.