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 , whose true value is unknown and whose uncertainty space (set of all possible/plausible values of ) is . Then the system is robust against the uncertainty in the true value of if it performs effectively as the value of the parameter varies over .
Robustness of this type is global in the sense that it is sought with regard to the performance of the system as varies over the entire uncertainty space .
In contrast, local robustness is a measure of the performance of the system in the locale (neighborhood) of a given nominal value of . Generally, a system that is globally robust is not necessarily locally robust at a given nominal value of , and vice versa. This distinction is similar to the distinction between a local and a global optimum.