According to INVESTOPEDIA:

What Does Robust Mean?
A characteristic describing a model’s, test’s or system’s ability to effectively perform while its variables or assumptions are altered. A robust concept can operate without failure under a variety of conditions.

So, the robustness of a system or a model, or a decision, is a measure of their ability to perform effectively while their variables or assumptions are altered.

Now, assume that the performance of a system is contingent on the value of a certain parameter, call it u, whose true value is unknown and whose uncertainty space (set of all possible/plausible values of u ) is \mathscr{U}. Then the system is robust against the uncertainty in the true value of u if it performs effectively as the value of the parameter varies over \mathscr{U}.

Robustness of this type is global in the sense that it is sought with regard to the performance of the system as u varies over the entire uncertainty space \mathscr{U}.

In contrast, local robustness is a measure of the performance of the system in the locale (neighborhood) of a given nominal value of u. Generally, a system that is globally robust is not necessarily locally robust at a given nominal value of u\in \mathscr{U}, and vice versa. This distinction is similar to the distinction between a local and a global optimum.

The radius of stability model is a staple model of local robustness, and the size criterion is an intuitive measure of global robustness.