A Lyapunov Characterization of Robust D-Stability with Application to Decentralized Integral Control of LTI Systems
John-Paolo Casasanta, John W. Simpson-Porco
TL;DR
This paper introduces Lyapunov-based necessary and sufficient conditions for robust D-stability, applying them to decentralized integral control in MIMO LTI systems to ensure stability amid network changes.
Contribution
It provides a novel Lyapunov characterization of robust D-stability and applies it to decentralized control, ensuring stability despite network reconfigurations.
Findings
Lyapunov conditions for robust D-stability are established.
Decentralized integral control stability is guaranteed under various network conditions.
The approach handles low-gain and arbitrary connection/disconnection scenarios.
Abstract
The concept of matrix D-stability plays an important role in applications, ranging from economic and biological system models to decentralized control. Here we provide necessary and sufficient Lyapunov-type conditions for the robust (block) D-stability property. We leverage this characterization as part of a novel Lyapunov analysis of decentralized integral control for MIMO LTI systems, providing sufficient conditions guaranteeing stability under low-gain and under arbitrary connection and disconnection of individual control loops.
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Taxonomy
TopicsStability and Control of Uncertain Systems · Control and Stability of Dynamical Systems · Neural Networks Stability and Synchronization