Time Moment Models
Time moment models of lumped linear time invariant systems are considered for identification of continuous time systems and the idea of “bias re-parameterization” introduced in the case of Markov parameter models is extended to the case of time moment models. The bias re-parameterization algorithm presented here for finitization of time moment sequence is effective in estimating irreducible models of MIMO systems. The proposed approach is also suitable for identification of structural invariants. With the present state-space description, this is equivalent to finding the order of each subsystem. In view of the decoupled estimation model, the order of any subsystem may be found by testing the rank of the associated Hankel matrix formed form the estimated time moments of the subsystem. By embedding prior knowledge of the modes (real/complex) of the system, it is shown in this chapter that it is possible to estimate good lower order approximations of even complex systems.