Gramian based model reduction of large-scale dynamical systems
(2000) Numerical Analysis 1999 — ISBN: [1-58488-020-1], p. 231-247, published
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- We describe model reduction techniques for large scale dynamical systems, modeled via systems of equations of the type ( F ( _ x(t); x(t); u(t)) = 0 y(t) = H(x(t); u(t)); as encountered in the study of control systems with input u(t) 2 < m , state x(t) 2 < N and output y(t) 2 < p . These models arise from the discretization of continuum problem and correspond to sparse systems of equations F (: ; : ; :) and H(: ; :). The state dimension N is typically very large, while m and p are usually reasonably small. Although the numerical simulation of such systems may still be viable for large state dimensions N , most control problems of such systems are of such high complexity that they require model reduction techniques, i.e. techniques that construct a lower order model via a projection on a state space of lower dimension. We survey such techniques and put emphasis on the case where F (: ; : ; :) and H(: ; :) are linear time-invariant or linear time-varying.
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Van Dooren, P. (2000). Gramian based model reduction of large-scale dynamical systems. In D.F. Griffiths and G.A. Watson (ed.), Numerical Analysis 1999 (p. p. 231-247). CRC Press. https://hdl.handle.net/2078.5/76283