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**Representation and control of infinite dimensional systems. Volume I.**
*(English)*
Zbl 0781.93002

The monograph contains mathematical control theory for general infinite- dimensional dynamical systems which are typically described by partial differential equations, functional differential equations or integral equations. The book is mainly dedicated to the control theory of linear infinite-dimensional dynamical systems. Using the methods of functional analysis, semigroups theory and linear operator theory the control and observation problems for infinite-dimensional systems are formulated and discussed. Special attention is paid on the theory of parabolic systems and systems with delays. The book contains the mathematical background on the theory of semigroups, linear operators and interpolation spaces. The relationships between different types of infinite-dimensional systems are explained, and representation theory is developed. Every chapter contains a separate list of references. The advanced mathematical theory is illustrated by several remarks comments and explanations. Finally, it should be mentioned, that the majority of the results presented in the monograph have been derived in the last years.

Reviewer: J.Klamka (Katowice)

### MSC:

93A10 | General systems |

93C25 | Control/observation systems in abstract spaces |

93B28 | Operator-theoretic methods |

93C20 | Control/observation systems governed by partial differential equations |

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |