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This work Introducing the empirical cross gramian matrix for state space reduction of large scale nonlinear control systems and derives the empirical joint gramian from the empirical cross gramian for combined state and parameter reduction for parametrized nonlinear control systems.
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This page is a summary of: Cross-Gramian-Based Combined State and Parameter Reduction for Large-Scale Control Systems, Mathematical Problems in Engineering, January 2014, Hindawi Publishing Corporation,
DOI: 10.1155/2014/843869.
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