The first five years of a phase theory for complex systems and networks

D Wang, W Chen, L Qiu - IEEE/CAA Journal of Automatica …, 2024 - ieeexplore.ieee.org
In this paper, we review the development of a phase theory for systems and networks in its
first five years, represented by a trilogy: Matrix phases and their properties; The MIMO LTI …

Phases of discrete-time LTI multivariable systems

X Mao, W Chen, L Qiu - Automatica, 2022 - Elsevier
In contrast to the well-developed gain analysis for multi-input-multi-output (MIMO) linear time-
invariant (LTI) systems, the research on the phase analysis does not share the same status …

[HTML][HTML] On the phases of a complex matrix

D Wang, W Chen, SZ Khong, L Qiu - Linear Algebra and its Applications, 2020 - Elsevier
In this paper, we define the phases of a complex sectorial matrix to be its canonical angles,
which are uniquely determined from a sectorial decomposition of the matrix. Properties of …

On the phases of a semi-sectorial matrix and the essential phase of a Laplacian

D Wang, X Mao, W Chen, L Qiu - Linear Algebra and its Applications, 2023 - Elsevier
In this paper, we extend the definition of phases of sectorial matrices to those of semi-
sectorial matrices, which are possibly singular. Properties of the phases are also extended …

Synchronization of diverse agents via phase analysis

D Wang, W Chen, L Qiu - Automatica, 2024 - Elsevier
In this paper, the synchronization of heterogeneous agents interacting over a dynamical
network is studied. The edge dynamics can model the inter-agent communications which …

Phase Preservation of -Port Networks under General Connections

J Chen, W Chen, C Chen, L Qiu - IEEE Transactions on …, 2024 - ieeexplore.ieee.org
This study first introduces the frequency-wise phases of-port linear time-invariant networks
based on recently defined phases of complex matrices. Such a phase characterization can …

New phase of phase

L Qiu, W Chen, D Wang - Journal of Systems Science and Complexity, 2021 - Springer
Year 2021 is special. It sees the renaissance of concept of phase and the birth of a phase
theory for matters much beyond complex numbers and single-input single-output (SISO) …

Converse theorems for integral quadratic constraints

SZ Khong, CY Kao - IEEE Transactions on automatic control, 2020 - ieeexplore.ieee.org
A collection of converse theorems for integral quadratic constraints (IQCs) is established for
linear time-invariant systems. It is demonstrated that when a system interconnected in …

When small gain meets small phase

D Zhao, W Chen, L Qiu - arXiv preprint arXiv:2201.06041, 2022 - arxiv.org
In this paper, we investigate the feedback stability of multiple-input multiple-output linear
time-invariant systems with combined gain and phase information. To begin with, we explore …

Gain and phase type multipliers for structured feedback robustness

A Ringh, X Mao, W Chen, L Qiu, SZ Khong - arXiv preprint arXiv …, 2022 - arxiv.org
It is known that the stability of a feedback interconnection of two linear time-invariant systems
implies that the graphs of the open-loop systems are quadratically separated. This …