This paper concerns a repetitive-control system with an input-dead-zone (IDZ) nonlinearity. First, the expression for the IDZ is decomposed into a linear term and a disturbance-like one that depends on the parameters of the dead zone. A function of the system-state error is used to approximate the combination of the disturbancelike term and an exogenous disturbance. The estimate is used to compensate for the overall effect of the IDZ and the exogenous disturbance. Next, the state-feedback gains are obtained from a linear matrix inequality that contains two tuning parameters for adjusting control performance; and the pole assignment method is employed to design the gain of a state observer. Then, two stability criteria are used to test the stability of the closed-loop system. The method is simple, employing neither an inverse model of the plant nor an adaptive control technique. It is also robust with regard to the different parameters of the IDZ, uncertainties in the plant, and the exogenous disturbance. Finally, two numerical examples demonstrate the effectiveness of this method and its advantages over others.
Stabilization of Repetitive Control System by Finite Spectrum Assignment Method