It is quite simple with a growth constraint, where you can directly specify the annual change coefficient.

However, note that the requirement that "emission in the current year is less than 5% of the previous year emission" is pretty tight: it means that in 10 years' time the emissions must reduce by 40% (0.95^10 ≈ 0.6).

Anyway, see example in the picture below:

There I assume that the emissions are represented by VAR_COMNET, and define the constraint requiring a 5% annual reduction, for all model years (IE=2 for UC_RHSRT, which defines a zero RHS constant for all years), because that seemed to correspond to what you described. It may well make the model infeasible, and so you may wish to consider starting the constraint at some later period (e.g. 2030), and/or using a smaller annual reduction.

To be more precise, consider what happens with your equation for the first year in the model horizon:

E(t) < E(t-1)*(1- 0.05)

For the first year t0, we would just get E(t0) < 0, because in the model there is no emission variable E(t) for t < t0. Therefore, you should obviously at least limit your constraint to years t > t0.

However, note that the requirement that "emission in the current year is less than 5% of the previous year emission" is pretty tight: it means that in 10 years' time the emissions must reduce by 40% (0.95^10 ≈ 0.6).

Anyway, see example in the picture below:

There I assume that the emissions are represented by VAR_COMNET, and define the constraint requiring a 5% annual reduction, for all model years (IE=2 for UC_RHSRT, which defines a zero RHS constant for all years), because that seemed to correspond to what you described. It may well make the model infeasible, and so you may wish to consider starting the constraint at some later period (e.g. 2030), and/or using a smaller annual reduction.

To be more precise, consider what happens with your equation for the first year in the model horizon:

E(t) < E(t-1)*(1- 0.05)

For the first year t0, we would just get E(t0) < 0, because in the model there is no emission variable E(t) for t < t0. Therefore, you should obviously at least limit your constraint to years t > t0.