Reduced-order model based on H-balancing for infinite-dimensional systems

Fatmawati, Roberd Saragih, Yudi Soeharyadi

Research output: Contribution to journalArticlepeer-review


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 (At; βBt;Ct) 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 (At;Bt;Ct) are equal and diagonal. This implies that the system (At;Bt;Ct) is H∞-balanced re-alization of the system (A;B;C). Based on the small H∞-characteristic values, the state variables of the system (At;Bt;Ct) 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 languageEnglish
Pages (from-to)405-418
Number of pages14
JournalApplied Mathematical Sciences
Issue number9-12
Publication statusPublished - 2013


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


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