Linear Time-Invariant Systems, Behaviors and Modules

This book comprehensively examines various significant aspects of linear time-invariant systems theory, both for continuous-time and discrete-time. Using a number of new mathematical methods it provides complete and exact proofs of all the systems theoretic and electrical engineering results, as well as important results and algorithms demonstrated with nontrivial computer examples. The book is intended for readers who have completed the first two years of a university mathematics course. All further mathematical results required are proven in the book.

1. A Survey of the Book's Content.- 2. The Language and Fundamental Properties of Behaviors.- 3. Observability, Autonomy and Controllability of Behaviors.- 4. Applications of the Chinese Remainder Theorem.- 5. Input/ Output Behaviors.- 6. Interconnections of Input/ Output Behaviors.- 7. The Transfer Matrix as Operator or Input/ Output Map.- 8. Stability via Quotient Modules.- 9. Compensators.- 10. Observers.- 11. Canonical State Space Realizations.- 12. Generalized Fractional Calculus.

ULRICH OBERST is Professor Emeritus at the University of Innsbruck, Austria. Earlier, he was professor of mathematics at the same university from 1972–2009. He completed his Ph.D. in Mathematics from the University of Munich, Germany, in 1965, under the guidance of Prof. F. Kasch who, in particular, taught injective co-generators—a notion from homological algebra which plays an important part in the present book.  He has visited a number of universities in several countries on invitations, including Pennsylvania State University, USA, University of California San Diego, USA, University of Chicago, USA, University of Florida, USA, and University of Rome II, Italy. His areas of interest include algebra and applied mathematics with special emphasis on constructive methods, in particular multidimensional linear systems theory and  discrete Gelfand, Fourier and Hartley transforms. A father of two and grandfather of six, Prof. Oberst is happily married to Karla. He is also an experienced piano player and has participated in two chamber music ensembles, playing piano trios, quartets and quintets with, in particular, string players from the Tyrolean Symphony Orchestra Innsbruck.