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The Versatile Cross Gramian for System Theoretic Model Reduction and More

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10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1

model reduction, model order reduction, controllability, observability, cross gramian, control system, system theory, reduced order modelling

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Abstract

For input-output systems, the cross gramian matrix encodes controllability and observability information into a single matrix, which are essential to system-theoretic applications. This system gramian can be used, in example, for model order reduction, sensitivity analysis, system identification, decentralized control and parameter identification. Beyond linear symmetric systems, the cross gramian is also available for parametric, non-symmetric, non-square and nonlinear systems.

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