• Smart Structures and Systems
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• v.21 no.2
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• pp.187-194
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• 2018

This paper focuses on the $H_{\infty}$ filter design problem for offshore steel jacket platforms. Its objective is to design a full-order state observer for offshore platforms in presence of unknown disturbances. To make the method more practical, it is assumed that the measured variables are available at discrete-time instants with time-varying sampling time intervals. By modelling the sampling intervals as a bounded time-varying delay, the estimation error system is expressed as a time-delay system. As a result, the addressed problem can be transformed to the problem of stability of dynamic error between the system and the state estimator. Then, based on the Lyapunov-Krasovskii Functional (LKF), a stability criterion is obtained in the form of Linear Matrix Inequalities (LMIs). According to the stability criterion, a sufficient condition on designing the state estimator gain is obtained. In the end, the proposed method is applied to an offshore platform to show its effectiveness.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.449-463
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• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.825-840
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• 2007

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.473-486
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• 2015

In this paper, we investigate a stability problem for a functional equation f(-x - y - z) - f(x + y) - f(y + z) - f(x + z) + 2f(x) + 2f(y) + 2f(z) - f(-x) - f(-y) - f(-z) = 0 by applying the direct method.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.199-209
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• 2002

In this paper, we investigate the problem of stability of the quadratic functional equation f(x+y+z)+f(y-z)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) on abelian group.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.827-831
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• 1987

The analysis of a certian example and simulations given in the previous sections show that the modified FKA is more stable than the standard FKA without loss of the performance of it. The general analysis of modified FKA's numerical stability is the open problem with more simulations in order to prove the stability of it.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.615-622
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• 2009

We solve the automatic continuity problem of an approximate higher derivation on a semisimple Banach algebra and investigate Hyers-Ulam stability for higher derivations.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.901-906
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• 1989

A robust stability problem for time delay systems is discussed by using a property of Lyapunov type operator equation. We propose a method to check the robust stability against the parameter perturbations occurring in both lumped parameter part and distributed delay element.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.471-477
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• 2003

In this paper we invstigate the new additive type functional equation f(2x - y) + f(x-2y) = 3f(x)-3f(y) and prove the stability problem for this equation in the spirit of Hyers, Ulam, Rassias and Gavruta.