• 대한수학회보
• /
• 제56권4호
• /
• pp.977-992
• /
• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.211-225
• /
• 2011

In this paper, a class of bi-directional associative memory (BAM) fuzzy cellular neural networks with distributed delays and impulses is formulated and investigated. By employing an integro-differential inequality with impulsive initial conditions and the topological degree theory, some sufficient conditions ensuring the existence and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

• 호남수학학술지
• /
• 제32권4호
• /
• pp.537-544
• /
• 2010

We prove the superstability of a functional inequality associated with general exponential functions as follows; ${\mid}f(x+y)-a^{x^2y+xy^2}g(x)f(y){\mid}{\leq}H_p(x,y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker.

• Journal of applied mathematics & informatics
• /
• 제30권5_6호
• /
• pp.1051-1065
• /
• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.420-424
• /
• 1993

New conditions for the exponential stability for both linear nonautnomous finite and a class of infinite dimensional systems described by parabolic partial differential equations (PDE's) are derived. The results for the parabolic systems are derived via semigroup approach.

• 충청수학회지
• /
• 제3권1호
• /
• pp.69-81
• /
• 1990

In this paper we investigate the problem of exponential asymptotic stability (EAS) in perturbed nonlinear systems of the differential system x' = f(t, x). Also, a simple method for constructing Liapunov functions is used to prove a kind of Massera type converse theorem.

• Kyungpook Mathematical Journal
• /
• 제56권2호
• /
• pp.517-527
• /
• 2016

In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권2호
• /
• pp.193-198
• /
• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• Journal of Electrical Engineering and Technology
• /
• 제8권6호
• /
• pp.1542-1550
• /
• 2013

This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1327-1335
• /
• 2011

This paper demonstrates that there is a unique exponentially stable equilibrium state of a class of impulsive cellular neural network with delays. The analysis exploits M-matrix theory and generalized comparison principle to derive some easily verifiable sufficient conditions for the global exponential stability of the equilibrium state. The results extend and improve earlier publications. An example with its simulation is given for illustration of theoretical results.