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**Representation and control of infinite dimensional systems.
2nd ed.**
*(English)*
Zbl 1117.93002

In the monograph linear infinite-dimensional control systems are considered. Controllability and observability conditions for distributed parameters and delayed systems are formulated and proved. In the proofs of the main results theory of linear semigroups and linear unbounded differential operators is extensively used. Several special cases are detaily studied and discussed. Moreover, linear quadratic control problems for these systems are defined and solved. Linear quadratic two-person zero-sum differential games are also considered. The monograph contains also mathematical background on the theory of semigroups of linear operators and interpolation spaces. As an illustrative examples control problems for parabolic equations and hyperbolic equations with distributed and boundary controls are investigated. The monograph presents a broad review of the existing results in control theory of infinite-dimensional dynamical systems. Theoretical results are illustrated by many examples and additional comments. The monograph contains extensive list of recent refernces concerning theory of abstract linear systems.

Finally, it should be pointed out that the monograph is the second edition of two-volume monograph published by the same authors in 1993. Many results in the one volume second edition are completely revised and corrected. Moreover, second edition contains many new research results.

Finally, it should be pointed out that the monograph is the second edition of two-volume monograph published by the same authors in 1993. Many results in the one volume second edition are completely revised and corrected. Moreover, second edition contains many new research results.

Reviewer: Jerzy Klamka (Gliwice)