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.

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Large scale systems with few inputs and outputs as compared to high order state variables occur frequently in Control systems. These systems have input-output union lead by a few states. The aim is to make use of those dominant states and to find a low rank approximation that is a better representation of original solution of Lyapunov equations. This approximation can be used in analysis, design and model reduction of control systems. In this paper a numerical method for computation of low rank approximation of Lyapunov equation is presented. The proposed method is based on Arnoldi Krylov subspace projection method with implicit restart scheme as a supplement to refine the results. Simulation of a system has been shown to validate the proposed technique.