A Phase Theory of MIMO LTI Systems
Abstract
In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes the well-known notions of positive real systems and negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the celebrated small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time-domain interpretations of phase-bounded systems via both energy signal analysis and power signal analysis. In addition, a sectored real lemma is derived for the computation of MIMO phases, which serves as a natural counterpart of the bounded real lemma.
Keywords
Cite
@article{arxiv.2105.03630,
title = {A Phase Theory of MIMO LTI Systems},
author = {Wei Chen and Dan Wang and Sei Zhen Khong and Li Qiu},
journal= {arXiv preprint arXiv:2105.03630},
year = {2022}
}