An Introduction to Infinite-Dimensional Linear Systems Theory

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.

Autorentext
Ruth F. Curtain (born Melbourne, Australia, 1941) completed her early academic education (B.Sc. (Hons) 1962, Dip.Ed. 1963, M.A. Mathematics 1965) at the University of Melbourne and a Ph.D. in Applied Mathematics at Brown University, Providence, R.I., USA in 1969. She was Assistant Professor at Purdue University from 1970 to 1971 and spent 1971 to 1977 at the Control Theory Centre, University of Warwick, UK. At present she is emeritus professor in the mathematics department of the University of Groningen where she has worked since 1977. Her research interests lie in the area of infinite-dimensional systems theory. She is the co-author of two books in this field: "Infinite Dimensional Systems Theory", LNCIS, volume 8, Springer Verlag, 1978, with A.J. Pritchard, and "An Introduction to Linear Infinite-Dimensional System Theory", Springer Verlag, 1995, with H.J. Zwart. She has served as associate editor for the international journals Systems and Control Letters, Automatica, the journal Mathematics of Control, Signals and Systems and the Journal of Mathematical Systems, Estimation and Control and as an editor for Automatica. For contributions to the control theory of stochastic systems and infinite-dimensional systems she was elected to the grade of Fellow in the IEEE in 1991.Hans Zwart (born Hoogezand-Sappemeer, The Netherlands, 1959) received his Masters degree in mathematics in 1984 and his Ph.D. in 1988 at the University of Groningen. Since 1988 he is with the Department of Applied Mathematics, University of Twente, the Netherlands, where he is now full professor. His research interest lies in the area of distributed parameter systems. In addition, he holds a part-time professorial position at the department of Mechanical Engineering, Eindhoven University of Technology. He is the co-author of many papers and of the text books "An Introduction to Linear Infinite-Dimensional System Theory", Springer Verlag, 1995, with R.F. Curtain and of "Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces" with B. Jacob. Current research topics include system theory for distributed parameter systems with a Hamiltonian dynamics and controller design for mechanical systems.

Inhalt
1 Introduction.- 1.1 Motivation.- 1.2 Systems theory concepts in finite dimensions.- 1.3 Aims of this book.- 2 Semigroup Theory.- 2.1 Strongly continuous semigroups.- 2.2 Contraction and dual semigroups.- 2.3 Riesz-spectral operators.- 2.4 Delay equations.- 2.5 Invariant subspaces.- 2.6 Exercises.- 2.7 Notes and references.- 3 The Cauchy Problem.- 3.1 The abstract Cauchy problem.- 3.2 Perturbations and composite systems.- 3.3 Boundary control systems.- 3.4 Exercises.- 3.5 Notes and references.- 4 Inputs and Outputs.- 4.1 Controllability and observability.- 4.2 Tests for approximate controllability and observability.- 4.3 Input-output maps.- 4.4 Exercises.- 4.5 Notes and references.- 5 Stability, Stabilizability, and Detectability.- 5.1 Exponential stability.- 5.2 Exponential stabilizability and detectability.- 5.3 Compensator design.- 5.4 Exercises.- 5.5 Notes and references.- 6 Linear Quadratic Optimal Control.- 6.1 The problem on a finite-time interval.- 6.2 The problem on the infinite-time interval.- 6.3 Exercises.- 6.4 Notes and references.- 7 Frequency-Domain Descriptions.- 7.1 The Callier-Desoer class of scalar transfer functions.- 7.2 The multivariable extension.- 7.3 State-space interpretations.- 7.4 Exercises.- 7.5 Notes and references.- 8 Hankel Operators and the Nehari Problem.- 8.1 Frequency-domain formulation.- 8.2 Hankel operators in the time domain.- 8.3The Nehari extension problem for state linear systems.- 8.4 Exercises.- 8.5 Notes and references.- 9 Robust Finite-Dimensional Controller Synthesis.- 9.1 Closed-loop stability and coprime factorizations.- 9.2 Robust stabilization of uncertain systems.- 9.3 Robust stabilization under additive uncertainty.- 9.4 Robust stabilization under normalized left-coprime-factor uncertainty.- 9.5 Robustness in the presence of small delays.- 9.6 Exercises.- 9.7 Notes and references.- A. Mathematical Background.- A.1 Complex analysis.- A.2 Normed linear spaces.- A.2.1 General theory.- A.2.2 Hilbert spaces.- A.3 Operators on normed linear spaces.- A.3.1 General theory.- A.3.2 Operators on Hilbert spaces.- A.4 Spectral theory.- A.4.1 General spectral theory.- A.4.2 Spectral theory for compact normal operators.- A.5 Integration and differentiation theory.- A.5.1 Integration theory.- A.5.2 Differentiation theory.- A.6 Frequency-domain spaces.- A.6.1 Laplace and Fourier transforms.- A.6.2 Frequency-domain spaces.- A.6.3 The Hardy spaces.- A.7 Algebraic concepts.- A.7.1 General definitions.- A.7.2 Coprime factorizations over principal ideal domains.- A.7.3 Coprime factorizations over commutative integral domains.- References.- Notation.