Numerical linear algebra aspects of control design computations.

*(English)*Zbl 0551.93025The 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.

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 |