Controllability of Multilayer Networked Sampled-data Systems

TL;DR

This paper investigates how the controllability of multilayer networked sampled-data systems is influenced by sampling strategies, network structure, and inter-layer couplings, providing conditions and examples for controllability under various scenarios.

Contribution

It offers new controllability conditions for multilayer sampled-data systems with inter-layer couplings, considering multi-rate sampling and network effects.

Findings

Controllability depends on sampling rates and network structure.

Inter-layer couplings can enable controllability even if a layer is uncontrollable.

Sampling modifications can positively or negatively impact system controllability.

Abstract

This paper explores the state controllability of multilayer networked sampled-data systems with inter-layer couplings, where zero-order holders (ZOHs) are on the control and transmission channels. The effects of both single- and multi-rate sampling on controllability of multilayer networked linear time-invariant (LTI) systems are analyzed, with some sufficient and/or necessary controllability conditions derived. Under specific conditions, the pathological sampling of single node systems could be eliminated by the network structure and inner couplings among different nodes and different layers. The representative drive-response inter-layer coupling mode is studied, and it reveals that the whole system could be controllable due to the inter-layer couplings even if the response layer is uncontrollable itself. Moreover, simulated examples show that the modification of sampling rate on local channels could lay a positive or negative effect on the controllability of the whole system. All the results indicate that the controllability of the multilayer networked sampled-data system is collectively affected by mutually coupled factors.