Cyclic Reformulation-Based System Identification for Periodically Time-Varying Systems

This paper presents a novel system identification algorithm for linear periodically time-varying (LPTV) plants within a discrete-time framework. The algorithm integrates a cyclic reformulation with a state coordinate transformation of the cycled system to enable precise identification of LPTV dynamics. Specifically, subspace identification methods are applied to the cycled signals, allowing the extraction of Markov parameters, which form the basis for constructing the state-space model. Furthermore, the sparsity properties of the matrices derived from these Markov parameters are analyzed and utilized to design the coordinate transformation matrix, enhancing the representation and interpretability of the identified LPTV model. Unlike conventional methods that rely on specific periodic input signals, the proposed approach leverages the inherent periodic structure of the system, eliminating such requirements and improving flexibility in practical applications. Numerical simulations are conducted to demonstrate the algorithm's effectiveness and accuracy in capturing the dynamic behavior of LPTV plants under realistic conditions, highlighting its potential for broad applicability.