Model inversion is essential in many control approaches, including inverse model feedforward and iterative learning control (ILC). The aim of this paper is the development of inversion techniques for linear periodically time-varying (LPTV) systems, possibly multivariable. The proposed method involves stable inversion, where bounded solutions are computed through a two-point boundary value problem. A key aspect herein involves a new dichotomic split for the stable and unstable dynamics, which is nontrivial for general LTV systems. As a special case, well-known stable inversion techniques for LTI systems are recovered. The approach is successfully demonstrated on a position-dependent wafer stage system.