ASYMPTOTIC STABILITY

[2] R. Sh. Liptser and A. N. Shiryayev, Theory of Martingales, Mathematics and Its Applications(Soviet Series), vol. 49, Kluwer Academic Publishers, Dordrecht, 1989.[3] A. V. Mel’nikov and A. E. Rodkina, Martingale approach to the procedures of stochastic approx-imation, Proceedings of the Third Fin[r]

t0Log1+Kμ(s)μ(s)Δs≤ exptt0−εΔsμ(s)−→ 0, t −→ ∞ . (2.92)Gro Hovhannisyan 17Remark 2.9. Comparing Lemmas 2.7 and 1.5 we see that nabla exponential functions ap-proach zero in the larger region (see (1.25)) in the complex plane than delta exponentialfunctions (see (2.87)). Thus asymptotic[r]

Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2007, Article ID 56350, 13 pagesdoi:10.1155/2007/56350Research ArticleExistence and Asymptotic Stability of Solutions for HyperbolicDifferential Inclusions with a Source TermJong Yeoul Park and Sun Hye ParkRec[r]

Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2007, Article ID 56350, 13 pagesdoi:10.1155/2007/56350Research ArticleExistence and Asymptotic Stability of Solutions for HyperbolicDifferential Inclusions with a Source TermJong Yeoul Park and Sun Hye ParkRec[r]

Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2010, Article ID 504670, 8 pagesdoi:10.1155/2010/504670Research ArticleGlobal Asymptotic Stability of Solutions toNonlinear Marine Riser EquationS¸ evket G¨urDepartment of Mathematics, Sakarya University, 5410[r]

5. ConclusionsThis article has studied the global asymptotic stability of a class of difference equations.The result obtained extends and generalizes some previous results. We are attempting toapply the technique used in this article to deal with other generic difference equationswhich i[r]

5. ConclusionsThis article has studied the global asymptotic stability of a class of difference equations.The result obtained extends and generalizes some previous results. We are attempting toapply the technique used in this article to deal with other generic difference equationswhich i[r]

Ni=1ε(Pi, 1) presented in Figure 11, is also well contained inside the regions of linearbehavior. In Figure 12, the trajectories of the system are plotted.Commennt 3.1. The application of all the proposed results to the same example, shows that the resultapplied in two steps (Theorem 2.6 and Corolla[r]

type impulsive neural networks,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 122–130, 2010.17 R. Rakkiyappan and P. Balasubramaniam, “On exponential stability results for fuzzy impulsiveneural networks,” Fuzzy Sets and Systems, vol. 161, no. 13, pp. 1823–1835, 2010.18[r]

ON THE RECURSIVE SEQUENCEE. CAMOUZIS, R. DEVAULT, AND G. PAPASCHINOPOULOSReceived 12 January 2004 and in revised form 29 May 2004Our aim in this paper is to investigate the boundedness, g lobal asymptotic stability, andperiodic character of solutions of the difference equation xn+1= (γx[r]

• Zergeroglu E., Dawson, D. M., Queiroz M. S. de, Krsti´c M., 2000, “Onglobal output feedback tracking control of robot manipulators”, in Proceed-ings of Conferenece on Decision and Control, Sydney, Australia, pp. 5073–5078.The controller called here, P“D” with gravity compensation and charac-terize[r]

q, are bounded. Moreover, thevector of joint velocities˙q goes asymptotically to zero.BibliographyThe analysis of global asymptotic stability of PD control for robots withoutthe gravitational term (i.e. with g(q) ≡ 0), is identical to PD control withcompensation of gravity and which wa[r]

Ki+ b<1. (1.20)As a consequence of Theorem 1.3, we have the following criterion for the global expo-nential stability of the zero solution of (1.10).Theorem 1.4. Suppose that there ex ist b>0 and µ∈ (0,1) such that (1.12), (1.16), and(1.20) hold. Then, the zero solution of (1.10[r]

2.(3:15)Collecting all above inequalities which imply X = 1 since ε > 0 is arbitrary, we com-plete the proof. □4 GeneralizationAs mentioned above, the global asymptotic stability of positive solutions to the variousequation listed above suggests that the same potentially holds f[r]

1School of Economics and Management, University of South China, Hengyang, Hunan 421001, People’s Republic ofChina2School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, People’s Republic ofChinaAuthors’ contributionsAll authors carried out the proof. All authors concei[r]

,yn= A +yn−1xn−ryn−s. Appl Math Comput. 176, 403–408 (2006). doi:10.1016/j.amc.2005.09.03910. Yalcinkaya, I: On the global asymptotic stability of a second-order system of difference equations. Discrete Dyn Nat Soc2008, 12 (2008). (Article ID 860152)11. Irićanin, B, Stević, S: Some sys[r]

RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVESTABILITY PROPERTIES OF STOCHASTIC VOLTERRAINTEGRO-DIFFERENTIAL EQUATIONSLEONID E. SHAIKHET AND JASON A. ROBERTSReceived 2 August 2004; Revised 16 January 2005; Accepted 10 April 2005We consider the reliability of some numerical methods in preserving th[r]

(t) < 0forallt ∈ T;(iii) moreover,ξc(t) = c for all right dense t ∈ T;(iv) for h>0, letT := hZ,thenμ(t) = h andξc(t) =exp(h · c)h(2.12)for all t∈ T, that is, t → ξc(t) is a constant function.3. Existence of a Lyapunov functionOur main result, the following theorem, is a necessary cond[r]

yxx7 Third equation of the system (1.14) is the yield condition Mohr-Coulomb written as stress component. 1.1.2.3. Bearing capacity of natural ground Prandtl (1920) was the first to solve the equations analytically for the case of problem on the ice when the foundation could not land at the weight[r]

that the matrix pairs (An , Bn ) and (A, B) have the same nilpotent structure in theWeierstraß-Kronecker canonical form (see, e.g. [9, 20, 21]).By using the data-dependence of the spectrum of the matrix pair (A, B) inProposition 4.6, the data-dependence of the exponential stability of equatio[r]