Error Bound for Non-Zero Initial Condition Using the Singular Perturbation Approximation Method

Adnan Daraghmeh and Naji Qatanani
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Adnan Daraghmeh: Department of Mathematics, Faculty of Science, An-Najah National University, Nablus 44830, Palestine
Naji Qatanani: Department of Mathematics, Faculty of Science, An-Najah National University, Nablus 44830, Palestine

Mathematics, 2018, vol. 6, issue 11, 1-16

Abstract: 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 ∞ 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 Antoulas et al. The theoretical results are validated numerically.

Keywords: reciprocal system; singular perturbation approximation; error bound; non-homogeneous system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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