Dynamic surface control of nonlinear systems

A method is proposed for designing stable controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems. This method is another “synthetic input technique”, similar to backstepping and multiple surface control methods, but with an important addition, r-1 low pass filters are included in the design, where r is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the “explosion of terms” that has made other methods difficult to implement in practice. This paper presents the method and proves stability via a composite Lyapunov method