Efficient system reduction modeling of periodic control systems with application to circuit problems

In this paper, we discuss an iterative method for the model order reduction of continuous linear time-varying (LTV) periodic descriptor systems where the system's matrices are singular. The model order reduction strategy proposed here is focused on the linear time-invariant (LTI) reformulation of the LTV model through suitable discretization scheme. The resulting LTI system is reduced using a balanced truncation method. We use the Low-Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration to approximate the solutions of the corresponding time-invariant Lyapunov equations. Due to the singularity of the system's matrices, we have used the Pseudo-inverses to find the optimal shift parameters that are used in LRCF-ADI approximation. The step responses, bode plots and eigenstructures of both the original and reduced system are compared to indicate the accuracy of the proposed model reduction approach.