Work

Feedback Stability Under Mixed Gain and Phase Uncertainty

Year: 2024

Type: article

Abstract: In this study, we investigate the robust feedback stability problem for multiple-input-multiple-output linear time-invariant systems involving sectored-disk uncertainty, namely, dynamic uncertainty subject to simultaneous gain and phase constraints. This problem is thereby called a sectored-disk problem. Employing a frequency-wise analysis approach, we derive a fundamental static matrix problem that serves as a key component in addressing the feedback stability. The study of this matrix problem heavily relies on the Davis–Wielandt shells of matrices, providing a profound insight into matrices subjected to simultaneous gain and phase constraints. This understanding is pivotal for establishing a less conservative sufficient condition for the matrix sectored-disk problem, from which we formulate several robust feedback stability conditions against sectored-disk uncertainty. Finally, several conditions based on linear matrix inequalities are developed for efficient computation and verification of feedback robust stability against sectored-disk uncertainty.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2024.3449689

Authors: Jiajin Liang, Di Zhao, Li Qiu

Institutions: Googol Technology (China), Tongji University, Hong Kong University of Science and Technology

Language: English

Topic: Stability and Control of Uncertain Systems

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Science, Technology and Innovation Commission of Shenzhen Municipality, Shenzhen Municipal Science and Technology Innovation Council

Awards: G2575069074, G4403542416