Approximation of Large-Scale Dynamical Systems
SIAM, 25.06.2009 - 510 Seiten
Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
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2-induced norm algorithm all-pass Antoulas Arnoldi balanced truncation balancing transformation Bode plots Butterworth filter characteristic polynomial Cholesky columns compute condition number continuous-time systems coprime decay rate decomposition defined denote diagonal discrete-time systems dynamical systems eigenvalues eigenvector equal error bound error systems example factorization Figure finite follows frequency Furthermore given Hankel matrix Hankel operator Hankel singular values Hankel-norm approximation Hº-norm imaginary axis implies impulse response input interpolation iteration Krylov methods Lanczos Lemma linear algebra linear system low rank Lyapunov equation Markov parameters minimal model reduction multiplicity nonsingular observability gramian obtained orthogonal output perturbation poles positive real proof Proposition rational interpolation reachability and observability reachability gramian realization reduced system reduced-order system result Riccati equation satisfy Schur SISO solution solving space square root stable subspace Sylvester equation symmetric system X Theorem transfer function upper bound upper triangular vector zero