EXPONENTIAL STABILITY

13 I. Chueshov and I. Lasiecka, “Inertial manifolds for von K´arm´an plate equations,” Applied Mathematicsand Optimization, vol. 46, no. 2-3, pp. 179–206, 2002.14 I. Chueshov and I. Lasiecka, “Long-time behavior of second order evolution equations with nonlineardamping,” Memoirs of the American[r]

On exponential stability of bidirectional associative memoryneural networks with time-varying delaysJu H. Parka,*, S.M. Leeb, O.M. KwoncaDepartment of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of KoreabPlatform Verification Division, BcN Bus[r]

 q0111/4, 0 <γ1k, γ1k< 2. It is easy to check that all conditions of Theorems 3.1 and 4.1 are satisfied.Hence, 5.1 has a unique equilibrium point, which is globally exponentially stable.6. ConclusionUsing the time-scale calculus theory, the homeomorphism theory and the Lyapunovfunc[r]

EXPONENTIAL STABILITY IN A SCALAR FUNCTIONALDIFFERENTIAL EQUATIONEDUARDO LIZ AND MIH´ALY PITUKReceived 21 March 2006; Revised 16 August 2006; Accepted 21 September 2006We establish a criterion for the global exponential stability of the zero solution ofthe scalar retarded[r]

EXPONENTIAL STABILITY OF DYNAMIC EQUATIONSON TIME SCALESALLAN C. PETERSON AND YOUSSEF N. RAFFOULReceived 6 July 2004 and in revised form 16 December 2004We investigate the exponential stability of the zero solution to a system of dynamic equa-tions on time scales. We do t[r]

Hindawi Publishing CorporationAdvances in Difference EquationsVolume 2009, Article ID 104310, 13 pagesdoi:10.1155/2009/104310Research ArticleExponential Stability of Difference Equations withSeveral Delays: Recursive ApproachLeonid Berezansky1and Elena Braverman21Department of Mathematics, Ben[r]

ASYMPTOTIC ESTIMATES AND EXPONENTIAL STABILITYFOR HIGHER-ORDER MONOTONE DIFFERENCE EQUATIONSEDUARDO LIZ AND MIH´ALY PITUKReceived 21 May 2004Asymptotic estimates are established for hig her-order scalar difference equations and in-equalities the right-hand sides of which generate a monotone sy[r]

Hindawi Publishing CorporationAdvances in Difference EquationsVolume 2011, Article ID 879649, 14 pagesdoi:10.1155/2011/879649Research ArticleExponential Stability of Two CoupledSecond-Order Evolution EquationsQian Wan and Ti-Jun XiaoShanghai Key Laboratory for Contemporary Applied Mathematics,[r]

ds, 1.10where x is a solution of 1.1, β and p are real parameters, the n × x matrices H, G1,andG2are positive definite, and t>0. The form of functionals 1.9 and 1.10 is suggestedby the functionals 1.7-1.8. Although many approaches in the literature are used to judgethe stabilit[r]

Hindawi Publishing CorporationAdvances in Difference EquationsVolume 2010, Article ID 540365, 18 pagesdoi:10.1155/2010/540365Research ArticleThe Existence and Exponential Stability forRandom Impulsive Integrodifferential Equations ofNeutral TypeHuabin Chen, Xiaozhi Zhang, and Yang ZhaoD[r]

[8] J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networkswith delays,” IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457–463, 2002.[9] J. Cao, J. Liang, and J. Lam, “Exponential stability of high-order bidirectional assoc[r]

time- and output-invariant, i.e., static perturbations. See [15, 26, 27, 29] for resultson stability radii of time-invariant linear systems. Earlier results for the robust stability of time-varying systems can be found, e.g., in [28, 30]. Therefore, it is naturalto extend the notion of[r]

This paper deals with the problem of global exponential stabilization for a
class of nonautonomous cellular neural networks with timevarying delays. The system
under consideration is subject to timevarying coefficients and timevaying delays. Two
cases of timevarying delays are considered: (i) the de[r]

3 J. J. Hopfield, “Neurons with graded response have collective computational properties like those oftwo-state neurons,” Proceedings of the National Academy of Sciences of the United States of America, vol.81, no. 10 I, pp. 3088–3092, 1984.4 B. Kosko, “Bidirectional associative memories,” IEEE T[r]

evolution equations on the half-line, Computers & Mathematics with Applications 42 (2001),no. 3–5, 301–311.[10] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1980.14 Exponential dichotomy[11] Y. Latushkin and Y. Tomilov, Fredholm differential operators with unb[r]

11 J. Huang, C. Li, and Q. Han, “Quasi-synchronization of chaotic neural networks with parametermismatch by periodically intermittent control,” in Proceedings of the WRI World Congress on ComputerScience and Information Engineering (CSIE ’09), vol. 6, pp. 485–489, 2009.12 J. H. Park, “Robust sta[r]

var ious advanced results on this problem have been reported [2 ,3]. Ho wever, almost allavailable results have been focused on systems with discrete delays. In reality, differencesystems with distributed delays become important because it is essential to formulatethe discrete-time analogue of the c[r]

and Applications 8 (1999), no. 3-4, 471–488.[11] S. Keller, Asymptotisches Verhalten invarianter Faserb¨undel bei Diskretisierung und Mittelwert-bildung im Rahmen der Analysis auf Zeitskalen, Dissertation, Universit¨at Augsburg, Augsburg,1999.[12] P. E. Kloeden and S. Hilger, The effect of time granu[r]

tion is to contrive the stability condition which does not include the information on the delay, and the other is the method which takes it into account. The former case is o en called the delay-independent criteria and generally provides simple algebraic condi-tions. In that sense, the ques[r]

ities do not work in the studies for nonlinear differential equations. With the develop-ment of the theory on nonlinear differential equations (e.g., see [14,15]), it is necessaryto study the corresponding nonlinear differential inequalities. In [16], the authorsdevelop a new nonlinear delay differe[r]