This chapter is intended to give a brief introduction to nonlinear control. Our objective is not to be comprehensive but to simply give some simple extensions of linear strategies that might allow a designer to make a start on a nonlinear problem. As far as possible, we will build on the linear methods so as to maximally benefit from linear insights. Summary So far, the entire book has dealt with linear system and controllers. The notion of transfer functions, poles, zeros and their respective cancellation is not directly applicable.
Stability becomes more involved.
Commutativity does not apply. As a consequence, the mathematics for nonlinear control become more involved, solutions and results are not as complete and intuition can fail more easily than in the linear case. Nevertheless, nonlinearities are frequently encountered and are a very important consideration. Non-smooth nonlinearities cannot in general be exactly compensated or linearized. The chapter applies a nonlinear generalization of the affine parameterization of Chapter 15 to construct a controller that generates a feedback linearizing controller if the model is smoothly nonlinear with stable inverse Nonlinear stability can be investigated using a variety of techniques.