• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.559-577
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• 2002

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.5-9
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• 1995

In many cases of robust stability problems, the characteristic polynomial has real coefficients which or nonlinear functions of uncertain parameters. For this set of polynomials, a new stability easily checking algorithm for reducing the conservatism of the stability bound are given. It is the new stability theorem to determine the stability region just in parameter space. Illustrative example show that the presented method has larger stability bound in uncertain parameter space than others.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.41-45
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• 1997

To design a control system, it is a elementary point that the stability of the system should be guaranteed. Also, the phase of the system plays an important role for its frequence performance. In this paper, we present two stability criterion of repetitive control system with phase-lead and lag compensator. First, the stability criterion for the servo control system with phase-lead and lag compensator is shown by using small-gain theorem. Second, for the repetitive control system with the compensator, the stability criterion, also, is determined by using small-gain theorem. Two stability criterions show the same results that the stability depends on a coefficient of the phase-lead and lag compensator under some condition in servo control system and repetitive control system.

• Journal of Power Electronics
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• v.9 no.1
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• pp.61-67
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• 2009

In this paper, a simple technique is presented for robust stability testing of perturbed DC-DC converters having multi-linear uncertainty structure. This technique provides a necessary and sufficient condition for testing robust stability. It is based on the corollary of Routh criterion and gridding of parameters. The previous work based on parametric control theory using Kharitonov's theorem and Hermite Biehler theorem gives conservative results and only the sufficient condition of stability, whereas the proposed method provides the necessary and sufficient condition for testing robust stability and it is computationally efficient. The superiority of the method is compared with the Edge theorem.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.525-538
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• 1998

Recently, a stability theorem for the Feynman integral as a bounded linear operator on$ L_2$($R^{d}$ /) with respect to measures whose positive and negative variations are in the generalized Kato class was proved. We study a stability theorem for the Feynman integral with respect to measures whose positive variations are in the class of $\sigma$-finite smooth measures and negative variations are in the generalized Kato class. This extends the recent result in the sense that the class of $\sigma$-finite smooth measures properly contains the generalized Kato class.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1115-1131
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• 2016

In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse h-stability theorem of Massera's type for the nonlinear impulsive systems by employing the $t_{\infty}$-similarity of the associated impulsive variational systems and relations.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.959-965
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• 1996

In this paper we study the index stability theorem for a bounded linear operator with closed range and extend the Kato's decomposition theorem for an absence of the index.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.