"Design of dynamics" simply refers to the use of feedback control to change the way a system responds to external influence.
In the cruise control example of slide 8, lecture 1, if there were no feedback (imagine cutting the signal that feeds back and subtracts from the reference), then the dynamics would be given by
m v' = -bv + k vdes + uhill
With the feedback, the closed-loop dynamics are modified to include a "-k v" term on the right hand side, which makes the car track a reference velocity much better.
In this case and in general, by our choice of controller, we are essentially designing the closed-loop system dynamics to have desirable properties. These properties are often specified in terms of how well a system output tracks a reference value.
Desirable properties can also be specified in terms of stability. Lecture slide 6 indicates "stability augmentation for highly agile, unstable aircraft" as an example of design of dynamics, and refers to using feedback control to change an unstable system into a stable one. These issues are discussed further in the "Flight Control" section (page 15) of the CDS Panel Report.