State-Space Modeling of Two-Dimensional Vector-Exponential Trajectories
We solve two problems in modeling polynomial vector-exponential trajectories dependent on two independent variables. In the first one we assume that the data-generating system has no inputs, and we compute a state representation of the most powerful unfalsified model for this data. In the second instance we assume that the data-generating system is controllable and quarter-plane causal, and we compute a Roesser input-state-output model. We provide procedures for solving these identification problems, both based on the factorization of constant matrices directly constructed from the data, from which state trajectories can be computed.
multidimensional systems; most powerful unfalsified model; Roesser models; bilinear differential forms