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This paper explores the use of reconfigurable intelligent surfaces (RISs) for moving target detection in multi-input multi-output (MIMO) radar. Unlike previous related works that ignore the propa-gation delay difference between the direct path and the RIS-reflected path, we examine the detection problem in RIS-assisted MIMO radar by taking into account the effect of asynchronous propagation. Specifically, we first develop a general signal model for RIS-aided MIMO radar with multiple asynchronous RISs and arbitrary wave-forms. Next, we formulate the RIS design problem by maximizing the overall received signal energy. The resulting optimization problem is non-convex, which is solved with semidefinite relaxation (SDR) techniques. A coherent detector is introduced for target detection. Finally, numerical results are presented to demonstrate the performance of the RIS-aided MIMO radar in comparison with the conventional MIMO radar.more » « less