##
**Linear system theory.
2nd ed.**
*(English)*
Zbl 0892.93002

Upper Saddle River, NJ: Prentice Hall. xv, 581 p. (1996).

The book being reviewed is a second edition [for the first edition see John Hopkins University Press XIV, p. 325 (1981; Zbl 0666.93065)]. Then new chapters on discrete-time time-varying linear systems are added. In addition, there are numerous improvements to the first edition by adding more examples and more drill exercises.

One feature of the book is to treat linear system theory mainly for time-varying linear systems and treat time-invariant linear systems as specializations. It covers most important topics on stability, controllability and observability, realizability, linear feedback and state observation. In the time-invariant case, polynomial fraction and geometric theory are also included.

Overall the book is beautiful done. The Notes section at the end of each chapter which suggests further reading is also a useful feature.

Conceptually, theories for continuous-time and discrete-time systems are very much the same. It is debatable whether it is wise to expand 10 chapters on discrete-time systems in this new edition. Traditionally, discrete-time systems are covered in digital control systems. Without detailed discussions on sampling operations and hold circuits, the values of the added portion on discrete-time systems are greatly reduced. They appear to be somewhat redundant. Like many books on linear system theory, most examples are of a contrived nature. Very few real-life application examples are given. The difficult issue of how to bridge the gap between theory and practice in teaching linear systems is still present in this book.

Nevertheless, this second edition is a welcome addition to the vast number of books on linear system theory. In fact it is a better one.

One feature of the book is to treat linear system theory mainly for time-varying linear systems and treat time-invariant linear systems as specializations. It covers most important topics on stability, controllability and observability, realizability, linear feedback and state observation. In the time-invariant case, polynomial fraction and geometric theory are also included.

Overall the book is beautiful done. The Notes section at the end of each chapter which suggests further reading is also a useful feature.

Conceptually, theories for continuous-time and discrete-time systems are very much the same. It is debatable whether it is wise to expand 10 chapters on discrete-time systems in this new edition. Traditionally, discrete-time systems are covered in digital control systems. Without detailed discussions on sampling operations and hold circuits, the values of the added portion on discrete-time systems are greatly reduced. They appear to be somewhat redundant. Like many books on linear system theory, most examples are of a contrived nature. Very few real-life application examples are given. The difficult issue of how to bridge the gap between theory and practice in teaching linear systems is still present in this book.

Nevertheless, this second edition is a welcome addition to the vast number of books on linear system theory. In fact it is a better one.

Reviewer: M.-Y.Wu (Boulder)

### MSC:

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

93C05 | Linear systems in control theory |