The use of linear filtering to simplify integrator backstepping control of nonlinear systems

A method is proposed for designing stable controllers with arbitrarily small tracking errors for uncertain mismatched nonlinear systems. This method utilizes the "integrator backstepping" approach but with an important addition, /spl gamma/-1 low pass linear filters, where /spl gamma/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model and model error bounds are not differentiated. This method is applied to both Lipschitz and nonLipschitz nonlinearities. The nonLipschitz case requires the use of signum functions and is illustrated with a numerical example.