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Numerical linear algebra aspects of control design computations. (English) Zbl 0551.93025

The interplay between recent results and methodologies in numerical linear algebra and mathematical software and their application to problems arising in systems, control, and estimation theory is discussed. The impact of finite precision, finite range arithmetic [including the implications of the proposed IEEE floating point standard(s)] on control design computations is illustrated with numerous examples as are pertinent remarks concerning numerical stability and conditioning. Basic tools from numerical linear algebra such as linear equations, linear least squares, eigenproblems, generalized eigenproblems, and singular value decomposition are then outlined.
A selected list of applications of the basic tools then follows including algorithms for solution of problems such as matrix exponentials, frequency response, system balancing, and matrix Riccati equations. The implementation of such algorithms as robust mathematical software is then discussed. A number of issues are addressed including characteristics of reliable mathematical software, availability and evaluation, language implications (Fortran, Ada, etc.), and the overall role of mathematical software as a component of computer-aided control system design.

MSC:

93B40 Computational methods in systems theory (MSC2010)
65F35 Numerical computation of matrix norms, conditioning, scaling
65G50 Roundoff error
15A12 Conditioning of matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93C05 Linear systems in control theory
15A18 Eigenvalues, singular values, and eigenvectors
65F20 Numerical solutions to overdetermined systems, pseudoinverses
93C15 Control/observation systems governed by ordinary differential equations
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