Control of Time-Delay Systems Based on Symmetric-Injection Virtual Reference Trajectory

An approach for the control of linear control systems with a single time-delay is proposed. The main contribution is the inclusion of a symmetric-injection virtual reference trajectory into the controller to render stability robustness of single-delay linear control systems. The dynamics of the virtual trajectory is included into the closed-loop dynamics allowing theoretical computation of the critical time-delay before losing stability. Moreover, an energy-based symmetry interpretation of the proposed approach is drawn. Numerical simulations considering stable and unstable linear systems are shown, and experiments to control a DC-motor with time-delay measurements validate our proposal.