Matrix Equations and Model Reduction

Model order reduction methods for linear time invariant systems are reviewed in this lecture. The basic ideas of the methods, such as the Padé approximation method, the rational interpolation method, the modal truncation method, the standard balanced truncation method, and the balancing related methods, are presented. The numerical algorithms of implementing the methods are discussed. For the balanced truncation method and the balancing related methods, Lyapunov equations or Riccati equations need to be solved. Algorithms for solving these matrix equations are introduced.