A parameterization for the class of all stabilizing repetitive learning controller for linear minimum phase systems

We give a parameterization of all causal stabilizing repetitive learning controllers for single-input and single-output linear minimum phase systems. The past studies on the parameterization of a repetitive learning control system were to obtain the parameterization of all internally stabilizing controllers for the control system such that the plant is connected 1/(1-e^-sT) in series. Since 1/(1-e^-sT ) has no zeros in the closed right half plane, also the serial connections of 1/(1-e^-sT) and a minimum phase system have no zeros in the closed right half plane. That is, the parameterization of all stabilizing controllers for a repetitive learning control system may be obtained by using the parameterization for a minimum phase system in Glaria and Goodwin (1994). Using the above mentioned idea, at first, the parameterization of all stabilizing repetitive learning controllers for the biproper minimum phase system is carried out. Next, since the exact repetitive learning controllers to stabilize the strictly stable proper system do not exist, the parameterization of all modified repetitive learning controllers using a low-pass filter in the repetitive learning controller is given