Mixed sensitivity H∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant (LTI) systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty (in form of multiplicative uncertainty). That uncertainty is approximated and then an H∞ based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞ controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.