# The Library

### INTRODUCTION TO SEMIGROUP THEORY

Tools

UNSPECIFIED.
(1993)
*INTRODUCTION TO SEMIGROUP THEORY.*
LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, 185
.
pp. 1-22.
ISSN 0170-8643

**Full text not available from this repository.**

## Abstract

In this paper some basic sytem theoretic concepts will be introduced for abstract systems of the form x(t) = Ax(t) + Bu(t), x(0) = x0, y(t) = Cx(t). (1)

Here A is the infinitesimal generator of a strongly continuous semigroup S(t) on a Banach space Z and necessary and sufficient conditions for this to be the case axe given by the Hille-Yosida theorem. For U another Banach space B is-an-element-of C(U, Z) and x0 is-an-element-of Z, u(.) is-an-element-of L2(0, infinity; U) a mild solution is defined to be x(t) = S(t)x0 + integral-t/0 S(t - s)Bu(s)ds (2) and x(.) is-an-element-of C(0; infinity; Z). Various definitions of controllablity, observability, stabilizability, detectability, identifiability and realizability will be given and theorems which characterize them will be stated. Throughout the paper examples will be given (albeit trivial ones) which illustrate the way the abstract definitions and results can be applied to concrete problems defined via partial differential equations and delay equations.

In preparing this introduction I have made considerable use of the following book by Ruth Curtain and Hans Zwart An Introduction to Infinite Dimensional Linear Systems Theory which is to be published soon.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > TL Motor vehicles. Aeronautics. Astronautics |

Journal or Publication Title: | LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES |

Publisher: | SPRINGER VERLAG |

ISSN: | 0170-8643 |

Official Date: | 1993 |

Volume: | 185 |

Number of Pages: | 22 |

Page Range: | pp. 1-22 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/21273 |

Data sourced from Thomson Reuters' Web of Knowledge

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