Controllability of Networked Sampled-data Systems

TL;DR

This paper investigates how sampling patterns affect the controllability of networked sampled-data systems, providing conditions under which controllability is preserved or lost, and highlighting the influence of network structure and node dynamics.

Contribution

It offers new controllability conditions for networked sampled-data systems considering multi-rate sampling and network structure design to mitigate pathological sampling effects.

Findings

Pathological sampling can be eliminated by network design.

Singular topology matrices cause controllability loss under sampling.

Periodic sampling does not affect controllability for certain node dynamics.

Abstract

The controllability of networked sampled-data systems with zero-order holders on the control and transmission channels is explored, where single- and multi-rate sampling patterns are considered, respectively. The effects of sampling on the controllability of networked systems are analyzed, with some necessary and/or sufficient controllability conditions derived. Different from the sampling control of single systems, the pathological sampling of node systems could be eliminated by an appropriate design of network structure and inner couplings. While for singular topology matrices, the pathological sampling of single nodes will cause the entire system to lose controllability. Moreover, any periodic sampling will not affect the controllability of networked systems with specific node dynamics. All the results indicate that whether a networked system is under pathological sampling or not is jointly determined by mutually coupled factors.