Laguerre-Gram Reduced-Order Modeling

Abstract : We present an efficient model reduction procedure based on the Laguerre description of the system to be approximated. Using a one-order operator defined in the Laplace domain we construct a pencil of functions and formulate the problem as the minimization of the ( L²) criterion. The use of a weight function in the inner product definition allows a control of the time-error spreading in model reduction procedure. We show how the required Gram matrix can be computed efficiently and prove that the impulse response of the reduced model is also in ( L²). The transfer function approach allows an immediate and promising application in model reduction of infinite dimensional systems. An extension to multiple-input-multiple-output systems is also given.
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2005, 50 (9), pp.1432-1435. 〈10.1109/TAC.2005.854653〉
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Ahmed Amghayrir, Noël Tanguy, Pascale Bréhonnet, Pierre Vilbé, Léon-Claude Calvez. Laguerre-Gram Reduced-Order Modeling. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2005, 50 (9), pp.1432-1435. 〈10.1109/TAC.2005.854653〉. 〈hal-00424216〉

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