ABSTRACT
This chapter summarizes a variety of control system normal forms published in the literature so that the normal forms which are derived in a similar framework with consistent notations. The system is nonlinear and the input is non-affine. The chapter addresses the family of systems which are the most general one relative to existing published normal forms of single input systems based on a similar approach. Starting from early 1990s, the research on normal forms moved in several related but different directions. For multi-input systems, their nonlinear normal forms and invariants were first studied in W. Kang. The quadratic normal form and quadratic invariants were derived in Reference for linearly controllable systems in which the controllability indices equal each other. Interested readers are referred to the related publications in the references for results on bifurcation control, invariants, symmetries, and practical stabilization of nonlinear systems based on normal form approach.
