VARIATION OF LYAPUNOV METHOD FOR DYNAMIC-SYSTEMS ON TIME SCALES

Date

1994-07-15

Author

KAYMAKCALAN, B
RANGARAJAN, L

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

201
views

0
downloads

A new comparison theorem that connects the solutions of perturbed and unperturbed dynamic systems in a manner useful to the theory of perturbations is given and this comparison theorem is employed as a stability criterion to compare the asymptotic behaviors of perturbed and unperturbed systems. It is further shown by means of both theory and numerical computation that time scales do offer a unification in order to emphasize the better asymptotic behavior of perturbed systems in both continuous and discrete cases. (C) 1994 Academic Press, Inc.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/64510

Journal

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

DOI

https://doi.org/10.1006/jmaa.1994.1254

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On Stability of Linear Delay Differential Equations under Perron's Condition Diblík, J.; Zafer, A. (Hindawi Limited, 2011) The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
Picone's formula for linear non-selfadjoint impulsive differential equations Ozbekler, A.; Zafer, Ağacık (Elsevier BV, 2006-07-15) In this paper, we derive a Picone type formula for second-order linear non-selfadjoint impulsive differential equations having fixed moments of impulse actions, and obtain a Wirtinger type inequality, a Leighton type comparison theorem, and a Sturm-Picone comparison theorem for such equations. Moreover, several oscillation criteria are also derived as applications. (c) 2005 Elsevier Inc. All rights reserved.
Stability of differential equations with piecewise constant arguments of generalized type Akhmet, Marat (Elsevier BV, 2008-02-15) In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367-383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and Sufficient conditions for stability of the zero Solution are ob...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
AN OPTIMAL-CONTROL PROBLEM WITH NONLINEAR ELLIPTIC STATE-EQUATIONS Leblebicioğlu, Mehmet Kemal (Elsevier BV, 1992-02-01) In this article some of the results for optimal control of linear systems have been generalized to a nonlinear case. This is achieved by employing standard techniques of the nonlinear theory. After demonstrating the existence of optimal controls, finite element method is used to discretize the problem. The resulting finite dimensional problem is solved by a special algorithm. The theoretical discussions are completed by proving that approximate solutions are reduced to exact solutions as the element size te...

Citation Formats

B. KAYMAKCALAN and L. RANGARAJAN, “VARIATION OF LYAPUNOV METHOD FOR DYNAMIC-SYSTEMS ON TIME SCALES,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 356–366, 1994, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64510.