Backstepping Forms of Multi-Input Nonlinear Systems

For a class of nonlinear systems with uncertainties the backstepping method[1,2]provides a recursive procedure to construct adaptive controllers or robust controllers includingnonlinear H∞ controllers. To apply these methods the systems should have certain forms. Forstatement ease we call those forms Canonical Backstepping Forms. For single-input systems thecanonical backstepping forms and the design of adaptive controllers via backstepping method arealready studied and well known[1]. The purpose of this paper is to investigate canonical backstepping forms of multi-input nonlinear systems. Block canonical forms are obtained. Then corresponding design methods of adaptive controls are presented.