Does anybody know which extensions to the linear controller exist that can cope with constraints in the output value and its derivative?
Usually, the plant being controlled have some limits and I wonder if there is something better than leaving a margin for overshoot, and decreasing the output if the rate of change is too high.
I would appreciate a reference from the engineering perspective/level.
Yes its called model predictive control (MPC). Matlab does have a toolbox for designing MPC controllers. However there is also a different toolbox, which I prefer, the Multi Parametric Toolbox (MPT). You can find a lot of papers about MPC and the MPT toolbox.
Hope this helps.