Structure Identifiability of an NDS with LFT Parametrized Subsystems

TL;DR

This paper establishes conditions under which the structure of a linear networked dynamic system with subsystems parametrized by linear fractional transformations can be uniquely identified from external measurements.

Contribution

It provides new sufficient and necessary conditions for NDS structure identifiability based on transfer function rank conditions and polynomial matrix rank criteria.

Findings

Identifiability is guaranteed if certain transfer function matrices have full normal rank.

A necessary and sufficient condition is derived for cases with no direct internal transmission.

A polynomial matrix rank condition depending on subsystem parameters is proposed for verification.

Abstract

Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle parameters (FPPs) through a linear fractional transformation (LFT). It has been proven that if in each subsystem, the transfer function matrix (TFM) from its internal inputs to its external outputs is of full normal column rank (FNCR), while the TFM from its external inputs to its internal outputs is of full normal row rank (FNRR), then the structure of the NDS is identifiable. Moreover, under some particular situations like there are no direct information transmission from an internal input to an internal output in each subsystem, a necessary and sufficient condition is established for NDS structure identifiability. A matrix valued polynomial (MVP) rank based equivalent condition is further derived, which depends affinely on subsystem (pseudo) FPPs and can be independently verified for each subsystem. From this condition, some necessary conditions are obtained for both subsystem dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a matrix pencil.