Comparing Polynomial and State-Space Models (System Identification Toolkit)

Selecting the correct model type and model order is crucial for successfully estimating a parametric model. In general, state-space models provide a more complete representation of the system, especially for multiple-input multiple-output (MIMO) systems, than polynomial models because state-space models are similar to first principle models that can provide more degree of freedom in describing MIMO systems.

The identification procedure for state-space models does not involve nonlinear optimization so the estimation reaches a solution regardless of the initial guess. Moreover, the parameter settings for the state-space model are simpler. You need to select only the order, or the number of states, of the model. The order can come from prior knowledge of the system. You also can determine the order by analyzing the singular values of the information matrix. However, the states that the state-space identification procedure identifies might not reflect the physical characteristics of a system accurately. Using a similarity transformation, you can identify equivalent models with states that better represent the system. Similarity transformations enable you to transform the states without misrepresenting the input-output behavior of the system.

When model order is high, state-space models are preferable to polynomial models. Polynomial models with high order might encounter numerical problems in computation.