Numerical methods for model reduction of periodic dynamical systems: Review and applications

EasyChair Preprint no. 547

Abstract

In the second-half of the past century the expeditious development of systems and control theory together with the achievements of digital control and signal processing have set the stage for a renewed interest in the study of periodic dynamical systems, specially in aerospace realm, control of industrial processes, mechanical systems, modeling of periodic time-varying filters and networks, circuit simulation, and multirate sampleddata systems, etc. These complicated systems are composed of large numbers of separate devices and they are described by very large mathematical models consisting of more and more mathematical systems with very large dimensions. Simulations of such systems can be unacceptably expensive and time-consuming due to limited computer memory and CPU consumption. The idea of model reduction is that the large models should be replaced by smaller models which are amenable to fast and efficient simulation and which still capture the devices’ input output behavior to an accepted accuracy. In this paper we review the different approaches for model reduction of time varying systems, and depict the numerical results showing the advantages and disadvantages of these approaches.

Keyphrases: Balanced truncation model reduction, Krylov approximation, Linear time-varying systems, Lyapunov equations, Model Order Reduction

@Booklet{EasyChair:547,
  author = {Mohammad Sahadet Hossain and Mohammad Monir Uddin},
  title = {Numerical methods for model reduction of periodic dynamical systems: Review and applications},
  howpublished = {EasyChair Preprint no. 547},

  year = {EasyChair, 2018}}