Design of a modified repetitive-control system with dynamic output-feedback controller

A linear-matrix-inequality (LMI) based method is presented in this paper to design a modified repetitive-control system with a dynamic output-feedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that converts the system design problem into a stabilization problem for a continuous-discrete 2D system. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. Using the singular-value decomposition of the output matrix, an LMI-based algorithm is derived to design the parameters of the controllers and feedback gains. Two tuning parameters in the LMI justify the choice of 2D control gains and thus enable the preferential adjustment of control and learning. Finally, a numerical example demonstrates the validity of the method.