Hyperstability of Control Systems

Popov, Vasile M.

ISBN 10: 3642656560 / ISBN 13: 9783642656569

Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2011

Translator(s): Georgescu, Radu. Series: Die Grundlehren der Mathematischen Wissenschaften. Num Pages: 400 pages, biography. BIC Classification: PB. Category: (P) Professional & Vocational. Dimension: 229 x 152 x 21. Weight in Grams: 582. . 2011. Softcover reprint of the original 1st ed. 1973. Paperback. . . . . Bestandsnummer des Verkäufers V9783642656569

Inhaltsangabe:

15 Liapunov’s "second method" eliminates this drawback and leads to accurate conclusions regarding the stability of well-defined families of systems. This method made it natural to introduce the new notion of "absolute stability" whose origin can be traced to a work of . A. I. Lur’e and V. N. Post­ nikov [1]. The results of the many investigations effected to date in the field of absolute stability have been presented in a number of monographs, from which we mention (in chrono­ logical order) . A. I. Lur’e [1], . A. M. Letov [1], . A. Halanay Fig. 1. 2 [1], M . . A . . Aizerman and F. R. Gantmacher [1] and S. Lef­ schetz [1]. Without going into a detailed exposition of these results (see the final chapter of this book), we shall discuss here only the manner in which one defines the families of systems that are studied. These systems are characterized by the fact that in Relation (4) - which describes the non-linear block B2 (Fig. 1. 1) - the function cp is continuous, vanishes for v = 0 and satisfies the inequality cp( v)v > 0 for every v =/= o. (6) In other words, the graph of function cp is entirely contained in the quadrants I and III; it may have, for instance, a shape similar to that shown in Fig. 1. 2. The object of the study of absolute stability consists in finding a criterion which secures simultaneously the stability of all the systems characterized by Condition (6) .

Reseña del editor: 15 Liapunov's "second method" eliminates this drawback and leads to accurate conclusions regarding the stability of well-defined families of systems. This method made it natural to introduce the new notion of "absolute stability" whose origin can be traced to a work of . A. I. Lur'e and V. N. Post­ nikov [1]. The results of the many investigations effected to date in the field of absolute stability have been presented in a number of monographs, from which we mention (in chrono­ logical order) . A. I. Lur'e [1], . A. M. Letov [1], . A. Halanay Fig. 1. 2 [1], M . . A . . Aizerman and F. R. Gantmacher [1] and S. Lef­ schetz [1]. Without going into a detailed exposition of these results (see the final chapter of this book), we shall discuss here only the manner in which one defines the families of systems that are studied. These systems are characterized by the fact that in Relation (4) - which describes the non-linear block B2 (Fig. 1. 1) - the function cp is continuous, vanishes for v = 0 and satisfies the inequality cp( v)v > 0 for every v =/= o. (6) In other words, the graph of function cp is entirely contained in the quadrants I and III; it may have, for instance, a shape similar to that shown in Fig. 1. 2. The object of the study of absolute stability consists in finding a criterion which secures simultaneously the stability of all the systems characterized by Condition (6) .

Bibliografische Details

Titel: Hyperstability of Control Systems
Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Erscheinungsdatum: 2011
Einband: Softcover
Zustand: New