Error bound for non-zero initial condition using the singular perturbation approximation method
Summary: In this article, we present up to date results on the balanced model reduction techniques for linear control systems, in particular the singular perturbation approximation. One of the most important features of this method is it allows for an a-priori \(L^2\) and \(H^\infty\) bounds for the approximation error. This method has been successfully applied for systems with homogeneous initial conditions, however, the main focus in this work is to derive an \(L^2\) error bound for singular perturbation approximation for system with inhomogeneous initial conditions, extending the work by \textit{A. C. Antoulas} [Approximation of large-scale dynamical systems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2005; Zbl 1112.93002)]. The theoretical results are validated numerically.
scientific article; zbMATH DE number 6994835