A Lyapunov Characterization of Robust D-Stability with Application to Decentralized Integral Control of LTI Systems
This work addresses stability issues in decentralized control systems, which is incremental as it builds on existing D-stability concepts with new Lyapunov characterizations.
The paper tackled the problem of robust D-stability in matrix theory and applied it to decentralized integral control for MIMO LTI systems, providing necessary and sufficient Lyapunov-type conditions and sufficient conditions for stability under low-gain and arbitrary loop changes.
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.