It is emphasised that this representation is valid globally and does not involve any restriction to the vicinity of the equilibrium points. Large transients and sustained non-equilibrium operation can both be accommodated. Realise a nonlinear controller with velocity-based linearisation family corresponding to the linear controller family designed at step 2. The gain-scheduled controller is not inherently confined to near equilibrium operation or subject to any slow variation constraint. This freedom is achieved while still retaining the divide and conquer approach and continuity with linear methods which is the principal advantage of the conventional gain-scheduling approach.
Dynamic inversion corresponds to the special case where the closed-loop dynamics are linear.
Indeed, in the case of purely linear systems, there is no scheduling variable and, consequently, plant measurements are not required to implement the pole-zero inverse. In this sense, it is closely related to the gain-scheduling methodology. However, it is emphasised that the velocity-based approach does not necessitate a slow variation requirement. A considerable body of results now exists relating to the design of controllers for plants which are in LPV or quasi-LPV form. Apparently lacking practical, generally applicable methods for carrying out such a transformation, a number of ad hoc approaches have been proposed in the literature.