Exploiting the structure of covariance matrices can effectively enhance the detection performance of adaptive detectors when insufficient independent and identically distributed (IID) training samples are available. In space-time adaptive processing (STAP) and multiple-input multiple-output (MIMO) radar, the covariance matrix of the clutter typically exhibits a Kronecker structure. Additionally, when the radar antenna is symmetrically configured, the covariance matrix possesses a persymmetric property. This paper investigates the target detection problem under the joint Kronecker and persymmetric structural constraints of the covariance matrix when limited training samples are aviable. By leveraging these structural properties and adopting a two-step generalized likelihood ratio test (GLRT) criterion, we propose an effective adaptive detector. Simulation results demonstrate that the proposed detector achieves superior detection performance in scenarios with limited training samples.