Robust controller design for lightly damped systems with feedback delay

A controller design method based on convex programming is used for lightly damped systems with feedback delay. The designed controllers are robust with respect to time delays in the feedback action, which is often crucial to the stability of lightly damped systems. Exogenous disturbances and unmodeled dynamics are taken into account. Since the convex program is a global optimal technique, once a controller is found, it is optimal in the sense that it meets the design specifications. On the other hand, if no solution is found, then there exists no linear, time-invariant controller which can satisfy the design specifications. Simulation results show that the designed controller can effectively stabilize the lightly damped system and significantly improve its performance.<>