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This book explores geometric control theory, illustrating the geometric and abstract algebra concepts used in linear geometric control. A set of running design examples is used to illustrate control synthesis problems of linear multivariable control.

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This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first

year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.

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Introduction.- Background.- Patterned LinearMaps.- System Properties.- Control Synthesis.- Ring Systems.- Chains.- Trees.- Future Research Directions.- Conclusion.

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From the reviews:
"This well-organized book is an extensive and complete introduction to patterned linear systems in the context of geometric control theory. The presentation of the material is elegant and in addition to giving basic results, the book adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. ... a useful reference book for graduate students and researchers focusing on systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems." (Long Wang, Mathematical Reviews, August, 2013)

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