COORDINATE TRANSFORMATION IN BACK-STEPPING DESIGN FOR A CLASS OF NONLINEAR-SYSTEMS

In this paper the problem of existence and construction of a co-ordinate transformation is investigated for non-linear systems appearing in feedback linearization and back-stepping adaptive control problems. Conditions are derived to completely characterize the classes of non-linear systems that are transformable to the simple triangular and parametric simple triangular forms via linear transformations. The conditions are shown to be invariant under linear co-ordinate transformations and non-linear feedback. For systems satisfying these conditions, the development of the co-ordinate transformation is shown to be equivalent to that of their first-order approximations and is straightforward.