Approximation of Large-Scale Algebraic Equations Using Implicit Restart Scheme

The numerical solution of large scale algebraic Lyapunov and Riccati equations is a vital issue in control systems analysis and design. It is a key step in many computational methods. In this paper a numerical method for computation of low rank approximation of large scale algebraic Lyapunov and Riccati equations is presented. This approximation can be used in model order reduction and design of large scale control systems. The proposed method is based on Arnoldi Krylov subspace projection method with implicit restart scheme as an enhancement to refine the results. Simulation of a system has been shown to authenticate the proposed technique. Results show good low rank approximation of large algebraic Lyapunov and Riccati equations can be obtained with minimal computational efforts.