Lyapunov equations approximation using implicit restart scheme

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