A note on the cross Gramian for non-symmetric systems

  • Himpe C
  • Ohlberger M
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The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric systems the cross gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to approximate a cross gramian for non-symmetric and non-square systems. To illustrate this new non-symmetric cross gramian, it is applied in the context of model order reduction.

Author-supplied keywords

  • Cross Gramian
  • controllability
  • decentralized control
  • model reduction
  • observability

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  • Mario OhlbergerWestphalian Wilhelm University Munster Institute of Numerical and Applied Mathematics

  • Christian Himpe

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