• 한국산업정보학회논문지
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• 제11권5호
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• 한국항공우주학회지
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• 제42권10호
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• pp.816-822
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• 2014

위성의 각속도를 추정하는 비선형 관측기의 설계방법을 제안한다. SDRE 기법을 이용하여 관측기를 설계하는데, 오차 수렴에 대한 충분조건을 제시하였다. 대수 Riccati 형태의 이 조건은, 비선형 항을 Lipschitz 형태로 변환하고 이에 대한 수렴 조건을 유도하여 구해진다. 이 조건으로부터 관측기의 게인을 구할 수 있으며, 시뮬레이션을 이용하여 제안한 방법을 검증하였다.

• 한국멀티미디어학회논문지
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• 제24권1호
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• pp.13-20
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• 2021

A Wasserstein GAN(WGAN), optimum in terms of minimizing Wasserstein distance, still suffers from inconsistent convergence or unexpected output due to inherent learning instability. It is widely known some kinds of restriction on the discriminative function should be considered to solve such problems, which implies the importance of Lipschitz continuity. Unfortunately, there are few known methods to satisfactorily maintain the Lipschitz continuity of the discriminative function. In this paper we propose techniques to stably maintain the Lipschitz continuity of the discriminative function by adding effective regularization terms to the objective function, which limit the magnitude of the gradient vectors of the discriminator to one or less. Extensive experiments are conducted to evaluate the performance of the proposed techniques, which shows the single-sided penalty improves convergence compared with the gradient penalty at the early learning process, while the proposed additional penalty increases inception scores by 0.18 after 100,000 number of learning.

• 대한수학회지
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• 제29권1호
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• pp.175-190
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• 1992

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• 충청수학회지
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• 제9권1호
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• pp.183-190
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• 1996

• 대한수학회보
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• 제51권1호
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• pp.67-76
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• 2014

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${\bullet}$ X is a divergence-free vector field satisfying the shadowing property. ${\bullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${\bullet}$ X is an expansive divergence-free vector field. ${\bullet}$ X has no singularities and is Anosov.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2099-2101
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• 2005

The problem of observer design for a class of Lipschitz nonlinear systems is considered. We propose a new observer design method which takes into account the structure of perturbed nonlinear terms with a scaling factor ${\epsilon}$. An example is provided to demonstrate the usefulness of our result over the existing method.

• 한국산업정보학회논문지
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• 제12권5호
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• 대한수학회지
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• 제37권5호
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• pp.835-847
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• 2000

We investigate various ${\Phi}$(t)-stability of comparison differential equations and we obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f(t, x).