Hyperstability of Control Systems Vasile M. Popov

ISBN: 9783642656569

Published: November 21st 2011

Paperback

400 pages


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Hyperstability of Control Systems  by  Vasile M. Popov

Hyperstability of Control Systems by Vasile M. Popov
November 21st 2011 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 400 pages | ISBN: 9783642656569 | 10.62 Mb

15 Liapunovs 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 beMore15 Liapunovs 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. Lure 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. Lure [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) .



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