• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.115-119
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• 1987

In this paper the observer design problem in bilinear systems is studied using the Walsh functions as approximating set of functions to find a finite series expansion of the state of bilinear system. A classical Liapnove method, to finding a class of observer feedback matrix, is applied to ensure uniform asymptotic stability of the observation error dynamics. An algorithm is derived for observer state eq. via Walsh function. The basic objective is to develop a computational algorithm for the determination of the coefficients in the expansion. This approach technique gives satisfactory result as well provides precise and effective method for the bilinear observer design problem.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2003.06a
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• pp.238-241
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• 2003

This paper presents a nonlinear least squares decision feedback equalizer Bilinear systems are attractive because of the ability to approximate a large class of nonlinear systems efficiently. The nonlinearity of channel is modeled using a bilinear system. The algorithms are derived by using the QR decomposition for minimization covariance matrix of prediction error by applying Givens rotation to the bilinear model. Result of computer simulation experiments that compare the performance of the bilinear DFE to two other DFE's in eliminating the intersymbol interference caused by a nonlinear channel are presented In the paper.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.487-494
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• 2019

We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ which leads to a complete formula of ${\parallel}f{\parallel}$ for every $f{\in}{\mathcal{L}}(^2l^3_{\infty})^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ is exposed.

• Proceedings of the Korea Information Processing Society Conference
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• 2021.11a
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• pp.232-235
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• 2021

동형암호는 서버에 암호화된 데이터를 통해 연산할 수 있다는 장점으로 대용량의 데이터를 암호화하여 처리하는 시스템에 사용될 수 있어 주목된다. 동형암호의 방법 중 효율성과 실용성을 지니는 장점으로 인해 연구되고 있는 Bilinear Pairing을 사용하는 서명 및 인증 방법들은 DDH와 CDH 문제에 기반을 둔 방법으로, 많은 연구가 진행되어 왔다. 본 논문은 동형암호에서 사용되는 Bilinear Pairing의 핵심인 GDH 그룹과 타원곡선암호, Weil Pairing, SDH 문제를 기반으로 하는 서명 방식과 그룹 서명 방식, 랜덤오라클을 제외한 서명을 소개한다.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.529-540
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• 2024

In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear Hörmander class $BS^{m}_{1,1}$ in variable Triebel-Lizorkin spaces and variable Besov spaces.

• Earthquakes and Structures
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• v.4 no.4
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• pp.397-428
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• 2013

This paper examines whether the "effective period" of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulselike excitations, the paper shows that the "effective period" = $T_{eff}$ of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system = $T_2$ is an even better approximation regardless the value of the dimensionless strength,$Q/(K_2u_y)=1/{\alpha}-1$, of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a "linear" vibration period has a marginal engineering merit.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.417-428
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• 2017

We classify the extreme bilinear forms of the unit ball of the space of bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.47-54
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• 2018

We classify the extreme, exposed and smooth bilinear forms of the unit ball of the space of bilinear forms on $l^2_{\infty}$.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.101-116
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• 2005

Using the iterative method, we derive an controller realization of the bilinear system, which is resulted from the system reformulation. We utilize Banach Fixed Point Theorem to support proposed controller, and the simulation results are also illustrated to verify usefulness of this technique.

• 전기의세계
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• v.30 no.11
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• pp.728-733
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• 1981

Most of real world systems are highly non-linear. But due to difficulties in analyzing and dealing with it, only the linear system theory is well estabilished. Bilinear system where state and control are linear but not linear jointly is introduced. Here shows that optimal state estimation of stochastic bilinear system requirs infinite dimensional filter, thus onesub-optimal estimator for this system is suggested.