Subspace Identification of Linear Time-Periodic Systems with Periodic Inputs

TL;DR

This paper introduces a novel subspace identification method for linear time-periodic systems with periodic inputs, leveraging frequency response of the time-lifted system to improve accuracy and consistency.

Contribution

It presents a new approach that overcomes frequency response computation issues in LTP systems by using a time-lifted LTI system framework, extending subspace identification techniques.

Findings

Method outperforms existing time-domain subspace methods

Proven to be consistent under mild noise conditions

Effective with ensemble of periodic input-output data

Abstract

This paper proposes a new methodology for subspace identification of linear time-periodic (LTP) systems with periodic inputs. This method overcomes the issues related to the computation of frequency response of LTP systems by utilizing the frequency response of the time-lifted system with linear time-invariant structure instead. The response is estimated with an ensemble of input-output data with periodic inputs. This allows the frequency-domain subspace identification technique to be extended to LTP systems. The time-aliased periodic impulse response can then be estimated and the order-revealing decomposition of the block-Hankel matrix is formulated. The consistency of the proposed method is proved under mild noise assumptions. Numerical simulation shows that the proposed method performs better than multiple widely-used time-domain subspace identification methods when an ensemble of periodic data is available.