Oberst U., Scheicher M., Scheicher I. Linear Time-Invariant Systems, Behaviors and Modules

Springer, 2020. — 755 p. — (Differential-Algebraic Equations Forum). — ISBN: 978-3-030-43935-4.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.A Survey of the Book’s Content
The Language and Fundamental Properties of Behaviors
Observability, Autonomy, and Controllability of Behaviors
Applications of the Chinese Remainder Theorem
Input/Output Behaviors
Interconnections of Input/Output Behaviors
The Transfer Matrix as Operator or Input/Output Map
Stability via Quotient Modules
Compensators
Observers
Canonical State Space Realizations of IO Systems via Gröbner Bases
Generalized Fractional Calculus and Behaviors