Decentralised fixed modes of networked MIMO systems

ABSTRACT

In this paper, decentralised fixed modes (DFMs) of a networked system are studied. The network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. The effects of the network topology, the node-system dynamics, the external control inputs, and the inner interactions on the existence of DFMs for the whole networked system are investigated. A necessary and sufficient condition for networked multi-input/multi-output (MIMO) systems in a general topology to possess no DFMs is derived. For networked single-input/single-output (SISO) LTI systems in general as well as some typical topologies, some specific conditions for having no DFMs are established. It is shown that the existence of DFMs is an integrated result of the aforementioned relevant factors which cannot be decoupled into individual DFMs of the node-systems and the properties solely determined by the network topology.

KEYWORDS:

• Networked system
• decentralised control
• decentralised fixed mode
• directed topology
• MIMO LTI system

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation (NNSF) of China [grant number 61225013], [grant number 11332001], [grant number 61673026] and the Hong Kong Research Grants Council [GRF grant number CityU 11208515].