Necessary and Sufficient Conditions on State Transformations That Preserve the Causal Structure of LTI Dynamical Networks

Abstract

Linear time-invariant (LTI) dynamic networks are described by their dynamical structure function, and generally they have many possible state space realizations. This work characterizes the necessary and sufficient conditions on a state transformation that preserves the dynamical structure function, thereby generating the entire set of realizations of a given order for a specific dynamic network.