ABSTRACT
This chapter presents the classical H. Poincare's approach to the problem of formal equivalence of dynamical systems. It provides the following W. Kang and A. J. Krener, the formal approach to nonlinear control systems. The chapter discusses a normal form for homogeneous systems, their invariants, explicit normalizing transformations and a normal form under a formal feedback. It describes a canonical form for nonlinear control systems and a dual normal form and a dual canonical form. The chapter reviews results of systems with controllable linearization and results on dynamical systems. It explores systems that are feedback equivalent to linear uncontrollable systems. The chapter explains applications of the formal approach to the classification of control systems and shows an enormous difference between the group of symmetries of feedback linearizable and nonlinearizable systems. It examines a class of analytic strict feedforward forms than can be transformed to a normal form via constructive analytic transformations.
