Linear Matrix Inequality-based Repetitive Controller Design for Linear Systems with Time-varying Uncertainties to Reject Position-dependent Disturbances

This paper addresses the problem of designing an optimal modified repetitive controller for a strictly proper plant with time-varying uncertainties to reject positiondependent disturbances. A modified repetitive controller with time-varying delay structure, inserted by a low-pass filter and an adjustable parameter, is developed for this class of system. Two linear matrix inequalities (LMIs)-based robust stability conditions of the closed-loop system with time-varying state delay are derived for fixed parameters. One is a delay-dependent robust stability condition that is derived based on the free-weight matrix. The other robust stability condition is obtained based on the H∞ control problem by introducing a linear unitary operator. To obtain the desired controller, the design problems are converted to two LMI-constrained optimization problems by reformulating the LMIs given in the robust stability conditions. The validity of the proposed method is verified through a numerical example.