Two-dimensional linear systems.

*(English)*Zbl 0593.93031
Lecture Notes in Control and Information Sciences, 68. Berlin etc.: Springer-Verlag. IX, 398 p. DM 62.00 (1985).

This book refers to the new and interesting area of 2-D (two-dimensional) systems. These systems have been studied in relation to several modern engineering fields such as 2-D digital filtering, seismic data processing, X-ray image enhancement, the enhancement and analysis of aerial photographs for detection of fires or crop damage, the analysis of weather photos, image deblurring, etc.

The book is devided in seven chapters. Overall, the book may be grouped into two sections. The first section includes chapters 1,2,3 and 4 and covers 2-D system theory concepts such as state-space models, transition matrices, response formulas, transfer functions, the realization problem, controllability, observability, reachability, stability and others. The second section includes chapters 5, 6 and 7 and covers feedback design techniques to solve various 2-D control problems such as characteristic polynomial and eigenvalue assignment, asymptotic and deadbeat observers, exact model matching, input-output decoupling, deadbeat control, the deadbeat servo problem, etc. Finally, an Appendix is included giving basic definitions, theorems and computational algorithms.

The book is very well written and organized and covers the various subjects mentioned previously very much in detail and in depth. It is highly suggested for those involved in multidimensional system theory, in control theory, in multidimensional filtering and other related areas. It is an invaluable monograph to have particular for graduate students and post-graduate researchers working in the area of multidimensional systems.

The book is devided in seven chapters. Overall, the book may be grouped into two sections. The first section includes chapters 1,2,3 and 4 and covers 2-D system theory concepts such as state-space models, transition matrices, response formulas, transfer functions, the realization problem, controllability, observability, reachability, stability and others. The second section includes chapters 5, 6 and 7 and covers feedback design techniques to solve various 2-D control problems such as characteristic polynomial and eigenvalue assignment, asymptotic and deadbeat observers, exact model matching, input-output decoupling, deadbeat control, the deadbeat servo problem, etc. Finally, an Appendix is included giving basic definitions, theorems and computational algorithms.

The book is very well written and organized and covers the various subjects mentioned previously very much in detail and in depth. It is highly suggested for those involved in multidimensional system theory, in control theory, in multidimensional filtering and other related areas. It is an invaluable monograph to have particular for graduate students and post-graduate researchers working in the area of multidimensional systems.

Reviewer: P.Paraskevopoulos

##### MSC:

93C35 | Multivariable systems, multidimensional control systems |

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93C05 | Linear systems in control theory |

93Bxx | Controllability, observability, and system structure |

93C55 | Discrete-time control/observation systems |

93D99 | Stability of control systems |

93E11 | Filtering in stochastic control theory |