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 …
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 …
invariant (LTI) systems, the research on the phase analysis does not share the same status …
[HTML][HTML] On the phases of a complex matrix
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 …
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
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 …
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 …
network is studied. The edge dynamics can model the inter-agent communications which …
Phase Preservation of -Port Networks under General Connections
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 …
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) …
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 …
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 …
time-invariant systems with combined gain and phase information. To begin with, we explore …
Gain and phase type multipliers for structured feedback robustness
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 …
implies that the graphs of the open-loop systems are quadratically separated. This …