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2020 | OriginalPaper | Chapter

2. A Survey of the Book’s Content

Authors : Ulrich Oberst, Martin Scheicher, Ingrid Scheicher

Published in: Linear Time-Invariant Systems, Behaviors and Modules

Publisher: Springer International Publishing

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Abstract

This chapter is a detailed comment on the content of the book and a self-contained survey over larger parts of linear time-invariant systems theory and electrical engineering, on the basis of mathematical knowledge of two university years. For simplicity, we restrict ourselves here to the continuous-time case over the complex field \({\mathbb {C}}\). We present the most important methods and results of the book and refer to the chapters or theorems, where they are discussed as well as to corresponding results in the literature. This chapter contains no proof and does not assume any knowledge from other chapters.

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Literature
1.
J.C. Willems, From time series to linear system. I. Finite-dimensional linear time invariant systems. II. Exact modelling. Automatica J. IFAC, 22(5 and 6), 561–580 and 675–694 (1986)
2.
L. Ehrenpreis, Fourier Analysis in Several Complex Variables (Wiley, New York, 1970)MATH
3.
B. Malgrange, Sur les systèmes différentiels à coefficients constants. In Les Équations aux Dérivées Partielles (Paris, 1962) (Editions du Centre National de la Recherche Scientifique, Paris, 1963), pp. 113–122
4.
V.P. Palamodov, Linear Differential Operators With Constant Coefficients (Springer, New York, 1970)CrossRef
5.
J.-E. Björk, Rings of Differential Operators (North-Holland Publishing, Amsterdam, 1979)
6.
7.
R.E. Kalman, P.L. Falb, M.A. Arbib, Topics in Mathematical System Theory (McGraw-Hill, New York, 1969)MATH
8.
H.H. Rosenbrock, State-Space and Multivariable Theory (Wiley, New York, 1970)MATH
9.
W.A. Wolovich, Linear Multivariable Systems. Applied Mathematical Sciences, vol. 11 (Springer, New York, 1974)
10.
J.W. Polderman, J.C. Willems, Introduction to Mathematical Systems Theory. A Behavioral Approach, Texts in Applied Mathematics, vol. 26 (Springer, New York, 1998)
11.
T. Kailath, Linear Systems (Prentice-Hall, Englewood Cliffs, 1980)MATH
12.
A.I.G. Vardulakis, Linear Multivariable Control. Algebraic Analysis and Synthesis Methods (Wiley, Chichester, 1991)
13.
C.T. Chen, Linear System Theory and Design (Harcourt Brace College Publishers, Fort Worth, 1984)
14.
R. Unbehauen, Elektrische Netzwerke: Eine Einführung in die Analyse (Springer, Berlin, 1987)CrossRef
15.
L.P. Schmidt, G. Schaller, S. Martius, Grundlagen der Elektrotechnik 3. Netzwerke (Pearson Studium, München, 2006)
16.
P.J. Antsaklis, A.N. Michel, Linear Systems, 2nd edn. (Birkhäuser, Boston, 2006)MATH
17.
D. Hinrichsen, A.J. Pritchard with the cooperation of F. Colonius, T. Damm, A. Ilchmann, B. Jacob, F. Wirth. Mathematical systems theory II. Control, Observation, Realization, and Feedback . Springer, to appear
18.
19.
F.M. Callier, C.A. Desoer, Multivariable Feedback Systems (Springer Texts in Electrical Engineering Springer. New York, 1982)
20.
L. Schwartz. Théorie des distributions. Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Hermann, Paris, nouvelle édition, entiérement corrigée, refondue et augmentée edition, 1966
21.
L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis. Grundlehren der Mathematischen Wissenschaften, vol. 256 (Springer, Berlin, 1983)
22.
M. Albach, Grundlagen der Elektrotechnik 2. Periodische und nichtperiodische Signalformen (Pearson Studium, München, 2005)
23.
24.
A. Kochubei, Y. Luchko, Handbook of Fractional Calculus with Applications. Vol. 1: Basic Theory, Vol. 2: Fractional Differential Equations. (De Gruyter, Berlin, 2019)
25.
H. Bourlès, B. Marinescu, U. Oberst, Weak exponential stability of linear time-varying differential behaviors. Linear Algebra Appl. 486, 523–571 (2015)MathSciNetCrossRef
26.
27.
R.G. Ballas, G. Pfeifer, R. Werthschützky, Elektromechanische Systeme in der Mikrotechnik und Mechatronik (Springer, Berlin, 2009)CrossRef
28.
K. Jantschek, Mechatronic Systems Design. Methods, Models, Concepts (Springer, Berlin, 2012)CrossRef
29.
D.C. Karnopp, D.L. Margolis, R.C. Rosenberg, System Dynamics. Modeling, Simulation, and Control of Mechatronic Systems (Wiley, Hoboken, 2012)CrossRef
30.
R.W. Newcomb, Network Theory, The State-Space Approach (Librairie Universitaire Louvain, Leuven, 1969)MATH
31.
M. Vidyasagar, Control System Synthesis: A Factorization Approach, MIT Press Series in Signal Processing, Optimization, and Control 7 (MIT Press, Cambridge, 1985)
32.
H. Bourlès, U. Oberst, Generalized convolution behaviors and topological algebra. Acta Appl. Math. 141, 107–148 (2016)MathSciNetCrossRef
33.
34.
I. Blumthaler, U. Oberst, Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules. Linear Algebra Appl. 436(5), 963–1000 (2012)MathSciNetCrossRef
35.
A. Quadrat, On a generalization of the Youla-Kučera parametrization. II. The lattice approach to MIMO systems. Math. Control Signals Systems, 18(3), 199–235 (2006)
36.
L. Pernebo, An algebraic theory for the design of controllers for linear multivariable systems. I. Structure matrices and feedforward design. II. Feedback realizations and feedback design. IEEE Trans. Automat. Control 26(1), 171–182 and 183–194 (1981)
37.
C.A. Desoer, M. Vidyasagar, Feedback Systems: Input-Output Properties (Academic Press, Cambridge, 1975)
38.
K. Zhou, J.C. Doyle, K. Glover, Robust and Optimal Control (Prentice-Hall, Upper Saddle River, 1996)
39.
I. Blumthaler, Stabilisation and control design by partial output feedback and by partial interconnection. Int. J. Control 85(11), 1717–1736 (2012)MathSciNetCrossRef
40.
H. Bourlès, Impulsive systems and behaviors in the theory of linear dynamical systems. Forum Math. 17(5), 781–807 (2005)MathSciNetCrossRef
41.
C. Bargetz, Impulsive solutions of differential behaviors. Master’s thesis, University of Innsbruck, 2008
42.
D.G. Luenberger, Observing the state of a linear system. IEEE Trans. Mil. Electron. 8(2), 74–80 (1964)CrossRef
43.
44.
R.F. Curtain, H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory (Springer, New York, 1995)CrossRef
45.
W.J. Rugh, Linear System Theory, 2nd edn. (Prentice-Hall, Upper Saddle River, 1996)MATH
46.
D. Hinrichsen, A.J. Pritchard, Mathematical Systems Theory I. Modelling, State Space Analysis, Stability and Robustness. Texts in Applied Mathematics, vol. 48 (Springer, Berlin, 2005)
47.
48.
H. Bourlès, B. Marinescu, U. Oberst, Exponentially stable linear time-varying discrete behaviors. SIAM J. Control Optim. 53(5), 2725–2761 (2015)MathSciNetCrossRef
49.
H. Bourlès, B. Marinescu, U. Oberst, The injectivity of the canonical signal module for multidimensional linear systems of difference equations with variable coefficients. Multidimens. Syst. Signal Process. 28(1), 75–103 (2017)MathSciNetCrossRef
50.
H. Bourlès, U. Oberst, Robust stabilization of discrete-time periodic linear systems for tracking and disturbance rejection. Math. Control Signals Syst. 28(3), Art. 18 (2016)
51.
U. Oberst, Two invariants for weak exponential stability of linear time-varying differential behaviors. Linear Algebra Appl. 504, 468–486 (2016)MathSciNetCrossRef
52.
U. Oberst, A constructive test for exponential stability of linear time-varying discrete-time systems. Appl. Algebra Eng. Comm. Comput. 28(5), 437–456 (2017)MathSciNetCrossRef
53.
J.-F. Pommaret, Partial Differential Control Theory. Vol. I. Mathematical Tools; Vol. II. Control Systems (Kluwer, Dordrecht, 2001)
54.
Metadata
Title
A Survey of the Book’s Content
Authors
Ulrich Oberst
Martin Scheicher
Ingrid Scheicher
Copyright Year
2020
Book
Linear Time-Invariant Systems, Behaviors and Modules

Print ISBN: 978-3-030-43935-4

Electronic ISBN: 978-3-030-43936-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43936-1_2

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