Positive 1D and 2D Systems

Citation

Rigelsford, J. (2002), "Positive 1D and 2D Systems", Industrial Robot, Vol. 29 No. 6. https://doi.org/10.1108/ir.2002.04929fae.003

Positive 1D and 2D Systems

Positive 1D and 2D Systems

T. KaczorekSpringer2002431 pp.ISBN 1-85233-508-4£60.00 (Hardback)

Keywords: Robotics, Linear systems

“Positive 1D and 2D Systems” is one of the latest additions to The Communications and Control Engineering series. The series reports the major technological advances in this field from academic and industrial institutions around the world. This is the first book devoted to positive multivariable 1D and 2D linear systems, and is based on the Author's P.h.D student lecture course. It comprises seven chapters focusing on two main areas, 1D and 2D positive linear systems.

Chapter 1, Positive Matrices and Graphs, discussed topics including: the Collate- Wielandt function; the canonical Frobenius form of a cyclic matrix; and graphs of positive systems. Externally and internally positive systems; the stability of positive systems; input-output stability; and composite positive systems, are amongst the topics addressed in Chapter 2,Continuous-Time and Discrete- Time Positive Systems.

Chapter 3 discusses Reachability, Controllability and Observability of Positive Systems, while the Realisation Problem of Positive 1D Systems is presented in Chapter 4. Topics addressed in these sections include: discrete-time and continuous-time systems; reachability and controllability of weakly positive systems with state feedback; basic notions and formulation of the realisation problem; and positive realisations in canonical forms of singular linear.

The three remaining chapters of the book focus on 2D systems and discuss 2D Models of Positive Linear Systems; Controllability and Minimum Energy Control of Positive 2D Systems; and the Realisation Problem for Positive 2D Systems. Topics presented in Chapters 5 and 6 include: internally and externally positive Roesser models; positive Fornasini-Marchesini models and relationships between models; and reachability and minimum energy control of positive 2D continuous-discrete systems.

The existence of positive realisation; determination of a positive 2D general model for a given transfer matrix; and concluding remarks and open problems, are amongst the topics discussed in Chapter 7.

Overall, this book is well written and provides comprehensive coverage of positive 1D and 2D system. It is unsuitable for readers without a strong mathematical background and is not a text into which a newcomer may dip into to get a feel for the subject. The book will be an invaluable reference text for postgraduate students and advanced practitioners of control systems and system modelling.

Jon Rigelsford