DocumentCode
756103
Title
A counterexample of a theorem by Tsolas et al. and an independent result by Zaborszky et al. [with reply]
Author
Zaborszky, J. ; Huang, Guo ; Zheng, Bao ; Varaiya, Pravin
Author_Institution
Dept. of Syst. Sci. & Math., Washington Univ., St. Louis, MO
Volume
33
Issue
3
fYear
1988
fDate
3/1/1988 12:00:00 AM
Firstpage
316
Lastpage
317
Abstract
Recent results on the composition of the stability boundary by N.A. Tsolas et al. (IEEE Trans. Circuits Syst., vol.CAS-32, no.10, pp.1041-9, Oct. 1985) and J. Zaborszky et al. (Proc. IFAC Symp. Power Syst. Power Plant. Contr., Beijing, China, Aug. 1986, pp.597-603) claimed that it consisted of the stable manifolds of index-one unstable equilibria and their closures. A counterexample shows the potential existence of additional structures within the boundary. This finding invalidates numerous theorems published in the literature. The author concedes that the counterexample to the theorem in the paper by N.A. Tsolas et al. is unassailable and identifies the error in his proof
Keywords
stability; index-one unstable equilibria; stability boundary; stable equilibrium points; stable manifolds; Bismuth; Constraint optimization; Convergence; Functional programming; Resource management; Set theory;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/9.414
Filename
414
Link To Document