Regularity/Controllability/Observability of an NDS with Descriptor Form Subsystems and Generalized LFTs

Abstract: This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional transformation (GLFT) of its parameters. Except a well-posedness condition, no any other constraints are put on either parameters or connections of a subsystem. Based on the Kronecker canonical form (KCF) of a matrix pencil, some matrix rank based necessary and sufficient conditions are established respectively for the regularity and complete controllability/observability of the NDS, in which the associated matrix depends affinely on both subsystem parameters and subsystem connections. These conditions keep the property that all the involved numerical computations are performed on each subsystem independently, which is attractive in the analysis and synthesis of a large scale NDS. Moreover, some explicit and easily checkable requirements are derived for subsystem dynamics/parameters with which a completely controllable/observable NDS can be constructed more easily.