Abstract
It is well known that sliding mode control theory is effective to nonlinear system. Up to now, there are many approaches proposed to design hyperplane in sliding mode control theory, such as eigenvalue placement method, optimal control method, frequency-shaped method and so on. However these design methods of hyperplane used for linear model, so it is impossible to construct a precise hyperplane to a nonlinear system. On the other hand, back-stepping method, which also belongs to the nonlinear control theory, bases on the Lyapunov stability theory. We propose a design method of hyperplane by using back-stepping method, so that the hyperplane is nonlinear and no approximation. An example and experimental results are provided to illustrate the design method of hyperplane. In addition, we use J. J. E. Slotine's sliding observers theory to estimate the state variables of nonlinear system.
