Design of non‐fragile guaranteed‐cost repetitive‐control system based on two‐dimensional model

This paper concerns a new method of repetitive control based on two‐dimensional (2D) system theory. First, a 2D model is presented that enables the independent adjustment of control, which happens within a repetition period, and learning, which happens between periods. Next, the problem of designing a repetitive‐control law is formulated as a state‐feedback design problem for the 2D model. An existence condition and a method of designing a robust repetitive‐control law for a plant containing time‐invariant structured uncertainties are established by combining 2D system theory with linear matrix inequalities. Then, based on those results, a non‐fragile guaranteed‐cost repetitive‐control law is derived. The controller gain to be designed is assumed to have additive gain variations. It guarantees that the value of a quadratic performance function is less than a specified upper bound for all admissible uncertainties. The main feature of this approach is that it enables the control action and the learning process to be adjusted independently by the direct tuning of the weighting matrices in the quadratic cost function. Finally, a numerical example demonstrates the validity of this approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society