In the design of robust controllers for complicated systems, model reduction fits several goals:
Finally, if a modern control method such as LQG or H∞ is used for which the complexity of the control law is not explicitly constrained, the order of the resultant controller is likely to be considerably greater than is truly needed. A good model reduction algorithm applied to the control law can sometimes significantly reduce control law complexity with little change in control system performance.
Model reduction routines in this toolbox can be put into two categories:
Additive error method — The reduced-order model has an additive error bounded by an error criterion.
Multiplicative error method — The reduced-order model has a multiplicative or relative error bounded by an error criterion.
The error is measured in terms of peak gain across frequency (H∞ norm), and the error bounds are a function of the neglected Hankel singular values.