  This paper presents a synthesis method for robust, regret optimal control.
The plant is modeled in discrete-time by an uncertain linear time-invariant
(LTI) system. An optimal non-causal controller is constructed using the nominal
plant model and given full knowledge of the disturbance. Robust regret is
defined relative to the performance of this optimal non-causal control. It is
shown that a controller achieves robust regret if and only if it satisfies a
robust $H_\infty$ performance condition. DK-iteration can be used to synthesize
a controller that satisfies this condition and hence achieve a given level of
robust regret. The approach is demonstrated three examples: (i) a simple
single-input, single-output classical design, (ii) a longitudinal control for a
simplified model for a Boeing 747 model, and (iii) an active suspension for a
quarter car model. All examples compare the robust regret optimal against
regret optimal controllers designed without uncertainty.
