Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems

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Abstract

In this paper, we consider the balanced truncation method for model reductions in large-scale linear and time-independent dynamical systems with multi-inputs and multi-outputs. The method is based on the solutions of two large coupled Lyapunov matrix equations when the system is stable or on the computation of stabilizing positive and semi-definite solutions of some continuous-time algebraic Riccati equations when the dynamical system is not stable. Using the rational block Arnoldi, we show how to compute approximate solutions to these large Lyapunov or algebraic Riccati equations. The obtained approximate solutions are given in a factored form and used to build the reduced order model. We give some theoretical results and present numerical examples with some benchmark models.

Keywords

Matrix Krylov subspaces Model reduction Dynamical systems 

Mathematics Subject Classification

65F 15A 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  1. 1.Université du Littoral, Côte d’OpaleCalais CedexFrance

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