Robust Nonlinear Control Design with Input and Measurement Disturbances

1 Introduction The robust control problem for uncertain nonlinear systems has received a great deal of attention in the last few years 1{7]. In most cases the problem addressed is robust stabilization or robust tracking, and knowledge of bounds on the uncertainties is assumed. Since such bounds are usually conservative, the gains employed in the resulting robust controllers are likely to be unnecessarily high. More recently, the problem of measurement disturbance attenuation in nonlinear systems has started to receive some attention. In 8], the authors solved this problem for the class of strict-feedback systems with additive measurement disturbances, while 9] considered both mul-tiplicative and additive measurement disturbances, but only for scalar nonlinear systems. In this paper we consider strict-feedback systems with multiplicative and additive bounded disturbances in both the state measurements and the control, and show that if the sign of the multiplicative disturbances is known, then it is possible to guarantee global uniform boundedness of the states, as well as regulation of the output to a neighborhood of the desired setpoint. Our design does not require knowledge of the disturbance bounds, and its gains can be as low as desired. Of course, since the disturbance bounds are unknown, the closed-loop states converge to an unknown compact residual set. Moreover, as the controller gains decrease, the size of this residual set increases, and thus asymptotic performance deteriorates.