The usefulness of the combination of the Lyapunov function technique and digital simulation for the stability analysis of dynamic systems is illustrated in two examples where the region of asymptotic sta bility is estimated by the analytical Lyapunov ap proach and established by a systematic search via digital simulation of the Lyapunov function. The ad vantage of the PACTOLUS simulator, with particular regard to man-to-machine interference, is empha sized.
Get full access to this article
View all access options for this article.
References
1.
R.E. KalmanJ.E. BertramControl system analysis and design via the "second method" of LyapunovJournal of Basic Engineering June 1960 pp 371-393
2.
Ibid pp 394-499
3.
4.
J. La SalleS. LefschetzStability by Lyapunov's direct method with applicationsMathematics in Science and Engineering vol 4Academic Press1961
5.
S. LefschetzStability of nonlinear control systemsMathematics in Science and Engineering vol 13Academic Press1965
6.
7.
N.G. ChetaevUstoichivost dvizenia-raboti po analiticheskoi mekhanike (The stability of motion; Studies in analytical mechanics)lzd Akad Nauk USSR (in Russian) Moscow1962
8.
Z.V. RekasiusJ.E. GibsonStability analysis of nonlinear control systems by the second method of LyapunovIRE Transactions on Automatic Control vol AC-7 no 1 January 1962 pp 3-15
9.
G.P. SzegöOn the application of Zhubov's method of constructing Lyapunov functions for nonlinear control systemsJournal of Basic Engineering ASME Paper 62-JACC-5 1963
10.
G.P. SzegöA contribution to Lyapunov's second method: nonlinear autonomous systemsJournal of Basic Engineering ASME paper 61-WA-192 1962
11.
D.G. SchultzJ.E. GibsonThe variable gradient method for generating Lyapunov functionsAIEE Transactions on Applications and Industry paper 62-81 September 1962
12.
R.D. BrennanH. SanoPACTOLUS—a digital analog simulator for the IBM 1620AFIPS Conference Proceedings vol 26 October 1964
13.
14.
15.
I.G. MalkinTeoria ustoichivosti dvizhenia (The theory of the stability of motion)U.S. Atomic Energy Commission1962 (English translation)
