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In the design of robust controllers for complicated systems, model reduction fits several goals:

To simplify the best available model in light of the purpose for which the model is to be used—namely, to design a control system to meet certain specifications.

To speed up the simulation process in the design validation stage, using a smaller size model with most of the important system dynamics preserved.

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.

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