This article is devoted to the antibump switched linear parameter varying (sLPV) controller design for morphing aircraft under delayed scheduling variables (or parameters), which is typically caused by lagging measurements of the morphing extent. Such delayed scheduling is formulated as the control disturbance and the asynchronous control in the sLPV scheme, according to whether the current mode governed by scheduling variables is correctly detected or not. The persistent dwell time (PDT) switching signals are utilized in this article to describe inherent slow and rapid switching phenomena for steady flight and fast morphing, respectively, which is more applicable than the conventional average dwell time (DT) or DT and covers them as special cases. By adopting the detected-mode-based Lyapunov functions and a smooth function, the stability condition is obtained for the underlying system, upon which the antibump sLPV controller allowing for delayed scheduling is designed, in contrast to the existing studies that simply ignore the detection lag to allow the use of overlapped partitions and scheduling-variable-dependent Lyapunov functions for different modes. By an aircraft with a variable-sweep wing and an aircraft with a deformable wingspan, the effectiveness and the superiority of the proposed approach are demonstrated via simulations.