Controllability and observability of multi-agent systems with general linear dynamics under switching topologies

Abstract

This paper investigates controllability and observability of multi-agent systems, in which all the agents adopt identical general linear dynamics and the interconnection topologies are switching. For controllability, criteria are established by virtue of the switching sequence and the constructed subspace sequence, respectively. Furthermore, controllability is considered from the viewpoint of graph theory, and distance partition and almost equitable partition are introduced into switching topologies to quantitatively analyse the controllable state set of the system. For observability, sufficient and/or necessary conditions are presented in terms of the system matrices and the associated invariant subspace. Finally, some numerical simulations are worked out to illustrate the theoretical results.

Keywords:

• Controllability
• observability
• graph partitions
• switching topologies
• multi-agent systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yongqiang Guan http://orcid.org/0000-0001-5580-1284

Notes

1 Of course, for different k and $v_{i_j}$, r and ${\mathbb{C}}_s$ are different. On the premise of not causing confusion, we use r and ${\mathbb{C}}_s$ for simplicity, $s=1,2,\dots ,r+1$.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 61751301, 61533001 and 61603288].