Research Article
Stability of General Dynamical Systems
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 184 - Issue 44 |
| Published: Jan 2023 |
| Authors: Mahadevaswamy B.S. |
10.5120/ijca2023922552
|
Mahadevaswamy B.S. . Stability of General Dynamical Systems. International Journal of Computer Applications. 184, 44 (Jan 2023), 1-17. DOI=10.5120/ijca2023922552
@article{ 10.5120/ijca2023922552,
author = { Mahadevaswamy B.S. },
title = { Stability of General Dynamical Systems },
journal = { International Journal of Computer Applications },
year = { 2023 },
volume = { 184 },
number = { 44 },
pages = { 1-17 },
doi = { 10.5120/ijca2023922552 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2023
%A Mahadevaswamy B.S.
%T Stability of General Dynamical Systems%T
%J International Journal of Computer Applications
%V 184
%N 44
%P 1-17
%R 10.5120/ijca2023922552
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In this paper comparison techniques are used to obtain sufficient condition for stability of an invariant set. Here sufficient conditions involving the stability of scalar differential equations and converse theorems for a reversible dynamical system proved and Two converse theorems for existence of a vector Lyapunov function in reversible dynamical system are proved. Concept of conditional invariancy is introduced. Sufficient condition for stability of conditional invariant are proved. Here introduced notion of conditional stability of a compact set.
References
- E.A. Barbashin: vc’ en zap M.G.V. no.135 pp.110-133 (1949) Russian.
- R. Bellman: Vector Lyapunov functions. J. SIAM Centro Ser. A1 (1962) pp.32-34, MR, Vol.26 (1963).
- N.P. Bhatia: Stability and Lyapunov functions in Dynamical Systems, Contributions to Differential equations, 3 (1964), pp.175-188, MR Vol.29 (1965).
- N.P. Bhatia and O. Hajek: Local semi-dynamical systems, Lecture notes in Mathematics (1969), Springer-verlag.
- N.P. Bhatia and G.P. Szego: Stability theory of Dynomical systems, Springer-Verlag, (1970).
- W. Hahn: Stability of Motion, Springer-Verlag (1967) Translated by Arne P. Baartsz, MR Vol.36 # 6716 (1968).
- A.A. Kayande and V. Lakshmikantam; General Dynamical systems and conditional stability, Proc. Cambridge Philos, Soc. 63 (1967), pp. 199-207, MR Vol. 34 # 6258 (1967).
- A.A. Kayande and V. Lakshmikantham: Conditional invariant sets and vector Lyapunov functions - J. Math. Anal. Appl. 14 (1966), pp.285-293, MR Vol. 32 # 7880 (1966).
- A.A. Kayande and V. Lakshmikantham: General dynamical systems and differential inequalities. Technical report, U.R.I. No.2 (1968).
- V.I. Zubov: The methods of A.M. Lyapunov and their applications (English translation) Noordhoff, (1964).
Index Terms
Keywords