• Transactions on Control, Automation and Systems Engineering
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• 제1권2호
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• pp.134-140
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• 1999

The robust generalized H2 filtering problem for a class of discrete time uncertain linear systems satisfying the sum quadratic constraints(SQCs) is considered. The objective of this paper is to develop robust stability condition using SQCs and design a robust generalized Ha filter to take place of the existing robust Kalman filter. The robust generalized H2 filter is designed based on newly derived robust stability condition. The robust generalized Ha filter bounds the energy to peak gain from the energy bounded exogenous disturbances to the estimation errors under the given positive scalar ${\gamma}$. Unlike the robust Lalman filter, it does not require any spectral assumptions about the exogenous disturbances . Therefore the robust generalized H2 filter can be considered as a deterministic formulation of the robust Kalman filter. Moreover, the variance of the estimation error obtained by the proposed filter is lower than that by the existing robust Kalman filter. The robustness of the robust generalized H2 filter against the uncertainty and the exogenous signal is illustrated by a simple numerical example.

• 충청수학회지
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• 제26권4호
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.149-161
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• 2011

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation: $$f({\frac{x+y}{2}})+f({\frac{x-y}{2}})=f(x)$$.

• 충청수학회지
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• 제28권3호
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• pp.353-363
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• 2015

In this paper, we investigate the functional equation f(3x+y)+f(3x-y) = f(x+2y)+2f(x-y)+6f(2x)+3f(x)-6f(y) and prove the generalized Hyers-Ulam stability for it in non-Archimedean normed spaces.

• 충청수학회지
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• 제20권4호
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• pp.503-514
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• 2007

In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

• 충청수학회지
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• 제27권2호
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• pp.261-269
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• 2014

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation $$(k+1)f(x+y)+f(x+{\sigma}(y))+kf({\sigma}(x)+y)-2(k+1)f(x)-2(k+1)f(y)=0$$ with an involution ${\sigma}$ for a fixed non-zero real number k with $k{\neq}-1$.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.509-517
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• 2016

In this paper, we consider the following functional equation with involution f(x + y) + f(x + σ(y)) = 2f(x) + f(y) + f(σ(y)) and prove the generalized Hyers-Ulam stability for it when the target space is a non-Archimedean Banach space.

• 대한수학회보
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• 제48권3호
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• pp.491-503
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• 2011

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.135-148
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• 2007

We prove the stability of generalized Jensen's equations in a Hilbert module over a unital $C^*$-algebra. This is applied to show the stability of a projection, a unitary operator, a self-adjoint operator, a normal operator, and an invertible operator in a Hilbert module over a unital $C^*$-algebra.

• 대한수학회보
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• 제42권1호
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.