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Tracking function approach to practical stability and ultimate boundedness
Author(s) -
Paradis W. O.,
Perlmutter D. D.
Publication year - 1966
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690120125
Subject(s) - liapunov function , stability (learning theory) , scalar (mathematics) , mathematics , function (biology) , control theory (sociology) , set (abstract data type) , computer science , nonlinear system , geometry , artificial intelligence , physics , control (management) , quantum mechanics , machine learning , evolutionary biology , biology , programming language
A graphical method of analysis is presented for studying the practical stability and ultimate boundeness of autonomous second‐order systems. It is argued that these measures of stability are in many cases more germane to design than Liapunov stability. The method incorporates much of the geometric character of a Liapunov analysis, but it is shown that a Liapunov function, relatively difficult to obtain, can be replaced by a set of easily postulated scalar functions which collectively yield the required stability information. Examples are given which demonstrate the use and effectiveness of the method.