WIAS Preprint No. 2339, (2016)

Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems


  • Redmann, Martin
    ORCID: 0000-0001-5182-9773
  • Freitag, Melina A.

2010 Mathematics Subject Classification

  • 93A15 93A30 15A24


  • model order reduction, balanced truncation, singular perturbation approximation, stochastic systems, Lévy process, Gramians, Lyapunov equations


When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.

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