GENERALIZED CONTROLLER CANONICAL-FORMS FOR LINEAR AND NONLINEAR DYNAMICS

A generalized controller canonical form is proposed for linear and nonlinear dynamics. It is obtained using the theorem of the primitive element from differential algebra. This area of mathematics, which was introduced in system theory in order to provide an answer to multivariable nonlinear input-output inversion, has also permitted a renewed understanding of synthesis problems, especially those involving control-dependent state transformations. Our derivation of the controller form does not apply to multivariable constant linear systems. This means, that in a certain sense, the structure of these systems is more complex than the structure of time-varying linear systems and of general nonlinear systems, unless we allow time-varying control-dependent linear transformations in the study of constant linear systems. Under our transformations, all nonlinear dynamics can be exactly linearized via dynamic feedback. The main departure from standard theory is that transformations may depend on input derivatives. Once differential-algebraic tools are introduced, the proofs of the results are easy. © 1990 IEEE