## Abstract

This paper presents a model reduction for unstable infinite dimen-sional system (A;B;C) using H∞-balancing. To construct H∞-balanced realization, we find a Lyapunov-balanced realizationof a normalized left-coprime factorization (NLCF) of the scaled system (A; βB;C). Next, we apply the new coordinate transformation to obtain yet another re-alization of NLCF system. This result is then translated to have the new scaled system (A^{t}; βB^{t};C^{t}) whichsimilar with (A; βB;C). Fur-thermore, it can be verified that the solutions of a control and ffilter H∞-Riccati operator equations of the system (A^{t};B^{t};C^{t}) are equal and diagonal. This implies that the system (A^{t};B^{t};C^{t}) is H∞-balanced re-alization of the system (A;B;C). Based on the small H∞-characteristic values, the state variables of the system (A^{t};B^{t};C^{t}) is truncated, to yield a reduced-order model of the system (A;B;C). To demonstrate the effectiveness of the proposed method, numerical simulations are ap-plied to Euler-Bernoulli beam equation.

Original language | English |
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Pages (from-to) | 405-418 |

Number of pages | 14 |

Journal | Applied Mathematical Sciences |

Volume | 7 |

Issue number | 9-12 |

Publication status | Published - 2013 |

## Keywords

- Coprime factorization
- H∞-balancing
- Reduced-order model
- Riccati equations
- infinite-dimensional systems

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