Linear systems theory. A structural decomposition approach.
This book presents various canonical forms for linear systems in continuous and discrete time and shows how such decompositions, called structural decompositions, have an impact on various design and synthesis problems. The first three chapters provide the necessary background in linear algebra and linear systems theory (controllability/observability, stability, invertibility, zeros, geometric methods, output injection). The next four chapters deal with several structural decompositions (the ones related to stability, the ones related to controllability and/or observability). The cases of descriptor systems and proper systems are detailed. The bilinear transformation relates continuous and discrete versions. The rest of the book deals with applications of these results. First, it is shown how the decompositions are instrumental for system factorizations (cascade factorizations). Then pole and zero placement issues are addressed. A weaker form of asymptotic time-scale assignment is considered. The conceptually related problems of disturbance decoupling and \(H_\infty\) control are the subject of another chapter. Finally, a MATLAB toolkit for the algorithms is presented. A bibliography (164 items) and an index are offered at the end. This good book on linear systems theory, which shows nicely how geometry underlies important control issues, is recommended.
scientific article; zbMATH DE number 2174323