I am just summarizing ddiez's answer with a small addition.
Robustness is the ability of the system to maintain its steady state or at the very least qualitative nature of the steady state with minor changes in the parameters of the system.
This is different from stability which actually means the ability of the system to return to its steady state when it is slightly displaced from there. A stable system will reach the steady state irrespective of the initial condition. In multistable systems the state where the system eventually converges, will depend on the initial condition.
So stability is meant in the sense of perturbation in the state and robustness, of perturbation in the system parameters.
So, if you have a model and you do a random sampling of parameters drawn from a uniform distribution of lets say ±2×mean, you will end up with a many sets of parameters with fluctuations from the mean values. Now, if you solve for the steady state at each parameter value you will get a distribution. Less the variance of this distribution, more robust is the system (based on the model).
We had discussed plasticity in this post. Plasticity may be in a way synonymous with adaptive; if a system takes an input and gives an output then how plastic a system is can be defined as how fast or easily does a system reach the new steady state. In this case the input is a parameter of the model and only that is changed.
If I put these concepts in the perspective of an organism's metabolism then:
- Robustness would refer to how (in)sensitive the metabolic flux is to the minor changes in rates of different reactions (by changes in the enzyme structures perhaps).
- Stability would refer to whether the system gets back (or how fast it gets back) to its original state if you add some extra or remove a metabolite.
- Plasticity would refer to how fast would the system adapt or reach the new steady state when there is a change of diet/available nutrients.
Having said that I also feel, as fileunderwater said, that definitions are not universal and different people mean different things. Mathematically speaking environment is an extrinsic parameter i.e. Input. Environmental robustness should mean the maintenance of the steady state response to changes in the input. This makes sense for example in the case of maintenance of body temperature in homeotherms. Environmental plasticity is also important in certain situations.