Laguerre-Gram reduced-order modeling

• Published in: IEEE transactions on automatic control Vol. 50; no. 9; pp. 1432 - 1435
• Main Authors: Amghayrir, A., Tanguy, N., Brehonnet, P., Vilbe, P., Calvez, L.-C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computer Science; Computer science; control theory; systems; Control theory. Systems; Engineering Sciences; Exact sciences and technology; Hilbert space; Industrial control; Infinite-dimensional systems; Laguerre functions; Micro and nanotechnologies; Microelectronics; MIMO; model-order reduction; Modeling and Simulation; Parameter estimation; Polynomials; Reduced order systems; Signal analysis; System identification; Transfer functions; Laplace operator; MIMO system; Infinite-dimensional systems; Laguerre function; Minimization; Laguerre polynomial; Infinite system; Modeling; model- order reduction; Pulse response; System description; Spreading; Weight function; Differential operator; Reduced order systems; Laplace transformation; Infinite dimension; Transfer function; Laguerre functions; model-order reduction
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.854653

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 L/sub /spl infin///sup 2/(/spl Ropf//sup +/) 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 L/sub /spl infin///sup 2/(/spl Ropf//sup +/). 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.