• Proceedings of the KIEE Conference
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• 2008.04a
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• pp.207-208
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• 2008

This paper presents a robust state observer design for a class of Lipschitz nonlinear systems with time delay and external disturbance. A sufficient conditions on the existence of the proposed observer are characterized by linear matrix inequalities. It is also shown that the proposed observer design can reduce the effect on the estimation error of external disturbance up to the prescribed level in spite of the existence of time delay. Finally, a numerical example is provided to verify the proposed design method.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.805-821
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• 2000

The paper deals with asymtotic stabillity of nonlinear nonautinomous systems by Lyapunov's direct method. The proposed Lyapunov-like function V(t, x) needs not be continuous in t and Lipschitz in x in a Banach space. The class of systems considered is allowed to be nonautonomous and infinite-dimensional and we relax the boundedness, the Lipschitz assumption on the system and the definite decrescent condition on the Lyapunov function.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1305-1314
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• 2010

In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations driven by a Brownian motion and the martingales of Teugels associated with an independent L$\acute{e}$vy process having a stochastic Lipschitz coefficient. We derive the existence and uniqueness of solutions for these equations via Snell envelope and the fixed point theorem.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.103-110
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• 1992

In this paper, T. Kawata's result[2] is generalized, by means of Beurling's norm, in the case of periodic stochastic processes of the second order which belong to Lipschitz class.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1083-1101
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• 2022

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.11
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• pp.1089-1093
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• 2008

This paper presents a robust state observer design for a class of Lipschitz nonlinear systems with time delay and external disturbance. Sufficient conditions on the existence of the proposed observer are characterized by linear matrix inequalities. It is also shown that the proposed observer design can reduce the effect on the estimation error of external disturbance up to the prescribed level in spite of the existence of time delay. Finally, a numerical example is provided to verify the proposed design method.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.15-33
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• 2024

In this article, we considered a class of nonlinear variational hemivariational inequality problems and investigated a gap function and regularized gap function for the problems. We discussed the global error bounds for such inequalities in terms of gap function and regularized gap functions by utilizing the Clarke generalized gradient, relaxed monotonicity, and relaxed Lipschitz continuous mappings. Finally, as applications, we addressed an application to non-stationary non-smooth semi-permeability problems.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.197-206
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• 2006

This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.255-261
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• 2000

This paper presents the results of the robust H(sub)$\infty$ FIR filtering for a class of nonlinear continuous time-varying systems subject to real norm-bounded parameter uncertainty and know Lipschitz nonlinearity under sampled measurements. We address the problem of designing filters, using sampled measurements, which guarantee a prescribed H(sub)$\infty$ performance in continuous time-varying context, irrespective of the parameter uncertainty and unknown initial states. The infinite horizon causal H(sub)$\infty$FIR filter are investigated using the finite moving horizon in terms of two Riccati equations with finite discrete jumps.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.99-116
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• 2017

The aim of this article is to introduce a new form of Kantorovich $Sz{\acute{a}}sz$-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.