An introduction to infinite-dimensional linear systems theory
Infinite-dimensional systems is now an established area of research with an expanding spectrum of applications. Given the recent trend in systems theory towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text that treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write such an introductory textbook suitable for a course on infinite-dimensional linear systems. An important consideration of the authors is that their book be accessible to both mathematicians and engineers with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix, and all the new theory is demonstrated on the same three physical examples: two distributed systems of a diffusion type and of a wave type, and a delay system. Since the aim is to enable students to apply the theory to distributed and delay systems commonly met in applications, each chapter has about 30 exercises testing both theoretical concepts and applications to examples of a physical nature. This feature and the integration of frequency-domain and state-space approaches make this book unique in the field of infinite-dimensional systems theory.
