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Normal form representation of control systems

This paper is to investigate the normal form representation of control systems. First, as numerical tools we develop an algorithm for normal form expression and the matrix representation of the Lie derivative of a linear vector field over homogeneous vector fields. The concept of normal form is modified. Necessary and sufficient conditions for a linear transformation to maintain the Brunowsky canonical form are obtained. It is then shown that the shift term can always be linearized up to any degree. Based on this fact, linearization procedure is proposed and the related algorithms are presented. Least square linear approximations are proposed for non‐linearizable systems. Finally, the method is applied to the ball and beam example.The efforts are focused on the numerical and computer realization of linearization process. Copyright © 2002 John Wiley & Sons, Ltd.