Precision tracking for non-minimum phase LPTV systems via a lifted time stable inversion

Feedforward control demonstrates the capacity of precision tracking in applications, typically necessitating the solution of the inverse model. For non-minimum phase systems with unstable internal dynamics, the inverse model yields unbounded inputs, impeding the implementation of the feedforward control method. Existing stable inversion leverages non-causal input and initial state transition to achieve exact tracking with an infinite time preview of the output. However, a limited preview window results in tracking errors, and the existence of the optimal transition relies on the invertibility of the Grammian matrix. Recently, a novel stable inversion based on lifting time systems has been introduced. It enables finite-time precision tracking without an infinite preview window and exhibits significant application potential, though confined to linear time-invariant systems. From the perspective of the lifted system, this paper addresses the stable inversion problem in finite time for multivariate linear periodic time-varying systems leveraging the equivalence between the linear periodic time-varying system and its lifted system. Simulation is designed to validate the effectiveness of the results.