Affine Dependence of Network Controllability/Observability on Its Subsystem Parameters and Connections

Tong Zhou, Yuyu Zhou

This paper investigates controllability/observability of networked dynamic systems (NDS) in which the system matrices of each subsystem are described by a linear fractional transformation (LFT). A connection has been established between the controllability/observability of an NDS and that of a descriptor system. Using the Kronecker canonical form of a matrix pencil, a rank based condition is established in which the associated matrix affinely depends on subsystem parameters and connections. An attractive property of this condition is that all the involved numerical computations are performed on each subsystem independently. Except a well-posedness condition, any other constraints are put neither on parameters nor on connections of a subsystem. This is in sharp contrast to recent results on structural controllability/observability which is proved to be NP hard. Some characteristics are established for a subsystem with which a controllable/observable NDS can be constructed more easily. It has been made clear that subsystems with an input matrix of full column rank are helpful in constructing an observable NDS that receives signals from other subsystems, while subsystems with an output matrix of full row rank are helpful in constructing a controllable NDS that sends signals to other subsystems. These results are extended to an NDS with descriptor form subsystems. As a byproduct, the full normal rank condition of previous works on network controllability/observability has been completely removed. On the other hand, satisfaction of this condition is shown to be appreciative in forming a controllable/observable NDS.

Knowledge Graph

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