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Control model uncertainty specifies how the behavior of a controlled plant may differ from a nominal model. A robust control claim is made over this allowed family. The description includes which parameters may change, their ranges, and which occurrences must represent the same physical quantity. It can also include unmodeled dynamics, such as an omitted actuator response, that cannot be represented by varying one constant coefficient.

Parametric model uncertainty retains a chosen equation form while allowing its parameters to vary. For an original example, a damped mass obeysHere $v$ is velocity and $u$ the applied-force control input. In the form $\dot{v}=av+bu$, the coefficients areTheir numerical ranges in consistent SI units are approximately $a\in [-2.222,-1.818]$ and $b\in [0.909,1.111]$, but they are not independent. The combination $a=-2.222$, $b=0.909$ does not correspond to one allowed mass. Replacing the physically linked family by the full rectangle of independent coefficient values introduces additional possible models.

This dependency matters when claiming robust stability or robust performance: enlarging the family may produce a more conservative test, while accidentally narrowing it can remove a genuinely possible failure. MathWorks's uncertain-parameter representation tracks the identity of named uncertain elements when they recur in a model.^[ref]

A bounded uncertainty set does not by itself assign probabilities. Saying $m\in [0.9,1.1]$ does not say that the endpoints are unlikely or that all masses are equally likely. It states what the guarantee must cover. Conversely, fitting the nominal mass from data does not prove that this interval covers every relevant operating condition.

The assumed time behavior is also part of the specification. An unknown but fixed mass and an arbitrarily time-varying coefficient are different model families. Likewise, uncertain gain does not automatically cover an unmodeled delay. A useful uncertainty description connects allowed mathematical variations to the physical mechanisms and measurements that justify them.