Topology and Subsystem Parameter Based Verification for the Controllability/Observability of a Networked Dynamic System

Abstract

This paper extends some recent results on the controllability/observability of networked dynamic systems (NDS) to a system 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 a 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 a matrix formed by the parameters of each subsystem and the subsystem connection matrix (SCM). One of the attractive properties of this condition is that in obtaining the associated matrices, all the involved numerical computations are performed on each subsystem independently, which makes the condition verification scalable for a NDS formed by a large number of subsystems. In addition, the explicit expression of the condition associated matrix on subsystem parameters and subsystem connections may be helpful in system topology design and parameter selections. As a byproduct, this investigation completely removes the full normal rank condition required in the previous works.