Iterative solvers for periodic matrix equations and model reduction for periodic control systems

Analysis and synthesis of periodic control systems for various engineering and mechanical problems are strongly related to the well known matrix equations, i.e., Lyapunov or Riccati equations. This paper presents the iterative methods for solving large-scale sparse projected discrete-time periodic Lyapunov equations which arise in periodic state feedback control problems and in model reduction of periodic descriptor systems. We extend the alternating direction implicit method and the Smith method to such equations and discuss their applications to the model reduction procedure for periodic descriptor systems. Numerical results are given to illustrate the efficiency and accuracy of the proposed methods.