• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.4 s.334
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• pp.15-20
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• 2005

Multi-Input, Multi-Output system suffers for the spatial channel correlation due to lack of spatial diversity. To overcome this defect, the antenna selection and switching system is proposed which selects the adequate antenna subset with highest channel diversity gain and switches the trasmission techniques according to channel environments. However. its performance analysis is insufficient due to the difficulty of modeling the spatial channel correlation. In this paper, the theoretical upper bound of symbol error probability is derived by using the statistical properties of Frobenius norm and minimum eigen-value of channel matrix. By computer simulation, it is shown that the derived theoretical upper bound is similar to the simulation results.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.483-490
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• 2004

The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that the existence of a mixed $H_2/H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_2$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.2
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• pp.10-18
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• 2003

This paper presents a method for designing guaranteed cost fuzzy filter with a desired H$_{\infty}$ disturbance rejection constraint of delayed fuzzy dynamic systems. This method not only guarantees an induced L$_2$ norm bound constraint on disturbance attenuation, but also minimizes an upper bound on a linear quadratic performance measure. A sufficient condition for the existence of guaranteed cost fuzzy filter with H$_{\infty}$ constraint is then presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.97-104
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• 2018

In this study, a structure satisfying the fatigue constraint is designed by applying the topology optimization based on the phase field design method. In order to predict life based on the stress value, high cycle fatigue failure theory in which stress acts within the range of elastic limit is discussed and three fatigue theories of modified-Goodman, Smith-Watson-Topper and Gerber theory are applied. To calculate the global maximum stress, a modified P-norm stress correction method is used. As a result, it is possible to obtain topology optimization results that minimize the volume while satisfying the fatigue constraints. By applying the phase field design method, a simple shape with a minimized gray scale was obtained, and the maximum stress value acting on the optimization result became very close to the allowable stress value due to the modified P-norm stress method. While previous studies does not consider the stress correction factor, this study proposes the determination method regarding the stress correction factor considering loading effects related to axial stress components.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.697-704
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• 2006

The paper is concerned with $H_{\infty}$ filtering for descriptor systems. A necessary and sufficient condition is established in terms of linear matrix inequalities(LMIs) for the existence of normal filters such that the error systems are admissible and the transfer function from the disturbance to the filtering error output satisfies a prescribed $H_{\infty}$-norm bound constraint. When these LMIs are feasible, an explicit parameterization expression of all desired normal filter is given. All these results are yielded without decomposing the original descriptor systems, which makes the filter design procedure simple and direct. Finally, a numerical example is derived to demonstrate the applicability of the proposed approach.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.9
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• pp.750-754
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• 2005

This paper deals with the design problem of multivariable PID controllers guaranteeing the closed-loop system stability and a prescribed $H_\infty$ norm bound constraint. We reduce the problem to the static output feedback stabilization problem. We derive a necessary and sufficient condition f3r the existence of PID controllers and we give an explicit formula of PID controllers. We also give an existence condition of PID controllers guaranteeing a prescribed decay rate. Finally, we give an LMI-based design algorithm, together with a numerical design example.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.3
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• pp.183-189
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• 2013

This paper presents a stabilization method for NCS (Networked Control Systems) with two additive time-varying delays. Each time delay component between the plant and the controller has different characteristics depending on communication network, and has the upper and lower bounds. The time delay occurring from the controller to the plant has an effect on the time delay occurring from the plant to the controller, and the relationship between two delays is taken into account on the stability analysis. Based on the two additive delay components and the bound conditions, the appropriate Lyapunov-Krasovskii functional and the LMI (Linear Matrix Inequality) method derive the stability condition and the $H_{\infty}$ norm constraint for time-varying delayed NCS. Simulation results are finally given to demonstrate the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.113-116
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• 1997

In this paper, we present a robust $H^{\infty}$ controller design method for parameter uncertain time-varying systems with disturbance and that have time-varying delays in both state and control. It is found that the problem shares the same formulation with the $H^{\infty}$ control problem for systems without uncertainty. Through a certain differential Riccati inequality approach, a class of stabilizing continuous controller is proposed. For parameter uncertainties, disturbance and time varying delays, proposed controllers the plant and guarantee an $H^{\infty}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Finally a numerical example is given to demonstrate the validity of the results.ts.