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**Computational methods for linear control systems.**
*(English)*
Zbl 0790.93001

Prentice Hall International Series in Systems and Control Engineering. New York etc.: Prentice Hall. xvii, 504 p. (1991).

The book presents an excellent survey on numerical methods for analysis and design of linear autonomous systems together with careful discussion of the propagation of rounding errors. Consequently, its first chapter covering a quarter (!) of this book is devoted to numerical matrix computations such as solution of linear equations, computation of eigenvalues and singular values etc.

The following six chapters are more closely related to topics of automatic control. However questions like the computation of the matrix exponential, the solution of the Lyapunov (Sylvester) equation or of the algebraic Riccati equation, computation of subspaces etc. are of importance also in other fields. Consequently, despite its narrowing title monograph is of interest and great value – and something like a ‘must’ – not only for engineers and mathematicians working in the control area but also for engineers and scientists working in other fields and – last but not least – also for applied mathematicians.

The authors present not only methods and discuss the various types of errors and their propagation but indicate also which software packages are available for certain tasks. There is only one minor objection – and at the same time request for a future edition: the authors should incorporate also a discussion of the use and benefits offered by interval computation, especially for problems of this type, [G. Ludyk, Automatisierungstechnik 37, No. 11, 415-423 (1989; Zbl 0698.93021)]. This will be important in view of the fact that by now not only programming languages like ALGOL-XSC are available but also software packages for control systems are coming up.

The following six chapters are more closely related to topics of automatic control. However questions like the computation of the matrix exponential, the solution of the Lyapunov (Sylvester) equation or of the algebraic Riccati equation, computation of subspaces etc. are of importance also in other fields. Consequently, despite its narrowing title monograph is of interest and great value – and something like a ‘must’ – not only for engineers and mathematicians working in the control area but also for engineers and scientists working in other fields and – last but not least – also for applied mathematicians.

The authors present not only methods and discuss the various types of errors and their propagation but indicate also which software packages are available for certain tasks. There is only one minor objection – and at the same time request for a future edition: the authors should incorporate also a discussion of the use and benefits offered by interval computation, especially for problems of this type, [G. Ludyk, Automatisierungstechnik 37, No. 11, 415-423 (1989; Zbl 0698.93021)]. This will be important in view of the fact that by now not only programming languages like ALGOL-XSC are available but also software packages for control systems are coming up.

Reviewer: I.Troch (Wien)

### MSC:

93-04 | Software, source code, etc. for problems pertaining to systems and control theory |

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93B99 | Controllability, observability, and system structure |

93C05 | Linear systems in control theory |

93B40 | Computational methods in systems theory (MSC2010) |