The aeroelastic stability of bridge decks equipped with multiple tuned mass dampers is studied. The problem is attacked in the time domain, by representing self-excited loads with the aid of aerodynamic indicial functions approximated by truncated series of exponential filters. This approach allows to reduce the aeroelastic stability analysis in the form of a direct eigenvalue problem, by introducing an additional state variable for each exponential term adopted in the approximation of indicial functions. A general probabilistic framework for the optimal robust design of multiple tuned mass dampers is proposed, in which all possible sources of uncertainties can be accounted for. For the purposes of this study, the method is also simplified in a form which requires a lower computational effort and it is then applied to a general case study in order to analyze the control effectiveness of regular and irregular multiple tuned mass dampers. A special care is devoted to mistuning effects caused by random variations of the target frequency. Regular multiple tuned mass dampers are seen to improve both control effectiveness and robustness with respect to single tuned mass dampers. However, those devices exhibit an asymmetric behavior with respect to frequency mistuning, which may weaken their feasibility for technical applications. In order to overcome this drawback, an irregular multiple tuned mass damper is conceived which is based on unequal mass distribution. The optimal design of this device is finally pursued via a full domain search, which evidences a remarkable robustness against frequency mistuning, in the sense of the simplified design approach.