\(H_\infty\) repetitive control of linear systems based on two-dimensional model (Q1037271)

Summary: This paper concerns with the \(H_\infty\) repetitive control of linear system based on Two-Dimensional (2D) system theory. First, a 2D model is established to describe the control behaviour within a repetition period and the learning process between periods. Next, the problem of designing an \(H_\infty\) repetitive control law is formulated as an \(H_\infty\) state-feedback design problem for the 2D model. A new existence condition and method of designing an \(H_\infty\) state-feedback control law for the 2D model is presented. Moreover, this idea is extended to solve the problem of \(H_\infty\) repetitive control law for linear system. Finally, a numerical example was presented to illustrate the effectiveness of the presented method.