Modelorder

Modelorder refers to the dimension or complexity of a mathematical model that describes a dynamical system. In practice it is often the number of independent state variables in a state-space representation, or equivalently the order of the differential equation that characterizes the system. For linear time-invariant models, the model order equals the dimension of the state vector and is closely tied to the number of poles in the transfer function.

In identification and modeling, choosing the appropriate model order is a balance between fidelity and simplicity. A model with too low an order may fail to capture essential dynamics, while an overly high-order model can overfit noise, become numerically unstable, and be difficult to interpret or use in control design. Orders are commonly specified or estimated for various model families, such as state-space models, autoregressive models with exogenous inputs, or rational transfer functions.

Model order reduction is a related field that aims to produce a lower-order model that preserves essential input-output behavior of a high-order system. Techniques include balanced truncation, Hankel-norm approximations, Krylov subspace methods, and Iterative Rational Krylov Algorithm (IRKA). These methods seek to retain dominant dynamics while discarding negligible modes, enabling simpler controllers, faster simulations, and reduced computational load.

Key considerations include identifiability, data quality, and the intended application. The chosen order should capture the significant dynamics without introducing unnecessary complexity. Understanding modelorder helps in model selection, validation, and the design of robust control or estimation strategies.