Phase Analysis of MIMO LTI Systems
Systems and Control
2019-04-09 v1 Dynamical Systems
Abstract
In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the frequency responses of which are cramped at all frequencies. This phase concept generalizes the notions of positive realness and negative imaginariness. We also define the half-cramped systems and provide a time-domain interpretation. As a starting point in an endeavour to develop a comprehensive phase theory for MIMO systems, we establish a small phase theorem for feedback stability, which complements the well-known small gain theorem. In addition, we derive a sectored real lemma for phase-bounded systems as a natural counterpart of the bounded real lemma.
Keywords
Cite
@article{arxiv.1904.03212,
title = {Phase Analysis of MIMO LTI Systems},
author = {Wei Chen and Dan Wang and Sei Zhen Khong and Li Qiu},
journal= {arXiv preprint arXiv:1904.03212},
year = {2019}
}