• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.4
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• pp.371-379
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• 1990

The decoupling problem has a great practical importance in that it simplifies greatly the control of a given system by reducing the multi-input multi-output systems. In this paper, we derive the necessary and sufficient conditions for decoupling 2-D F-MM II via state feedback. For the general case, the problem of determining the feedback matrix F involves the solution of nonlinear algebraic equations. Under certain conditions, however, it is shown that an explicit formula for F may be derived. In comparsion with the method for FM, it appears that this method for F-MM II is more general and the algorithm is simpler.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1215-1235
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• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• Smart Structures and Systems
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• v.29 no.5
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• pp.677-691
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• 2022

Water cycle algorithm (WCA) has been a very effective optimization technique for complex engineering problems. This study employs the WCA for simultaneous prediction of heating load (L_H) and cooling load (L_C) in residential buildings. This algorithm is responsible for optimally tuning a neural network (NN). Utilizing 614 records, the behavior of the L_H and L_C is explored and the captured knowledge is then used to predict for 154 unanalyzed building conditions. Since the WCA is a population-based algorithm, different numbers of the searching agents were tested to find the most optimum configuration. It was observed that the best solution is discovered by 500 agents. A comparison with five newly-developed benchmark optimizers, namely equilibrium optimizer (EO), multi-tracker optimization algorithm (MTOA), slime mould algorithm (SMA), multi-verse optimizer (MVO), and electromagnetic field optimization (EFO) revealed that the WCANN predicts the desired parameters with considerably larger accuracy. Obtained root mean square errors (1.4866, 2.1296, 2.8279, 2.5727, 2.5337, and 2.3029 for the L_H and 2.1767, 2.6459, 3.1821, 2.9732, 2.9616, and 2.6890 for the L_C) indicated that the most reliable prediction was presented by the proposed model. The EFONN, however, provided a more time-effective solution. Lastly, an explicit predictive formula was elicited from the WCANN.

• 한국태양에너지학회:학술대회논문집
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• 2011.11a
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• pp.278-281
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• 2011

This system can predict the maximum output about all illumination levels so that the PV system designer can design the system having the best efficiency. For the output prediction exact about the solar cell, that is the device the basis most in the PV system, the basis has to be in order to try this way. The solution based on Lambert W-function are presented to express the transcendental current-voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. A simple and efficient method for the extraction of a single current-voltage (I-V) curve under the constant illumination level is proposed. With the help of the Lambert W function, the explicit analytic expression for I is obtained. And the explicit analytic expression for V is obtained. This analytic expression is directly used to fit the experimental data and extract the device parameters. The I-V curve of the solar cell was expressed through the modeling using Lambert W-function and the numerical formula where there is the difficulty could be logarithmically expressed This method expresses with the I-V curve through the modeling using Lambert W-function which adds other loss ingredients to the equation2 as to the research afterward. And the solar cell goes as small and this I-V curve can predict the power penalty in the system unit.

• Steel and Composite Structures
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• v.29 no.3
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• pp.333-348
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• 2018

An analytical method is developed for analysing the contact buckling response of infinitely long, thin corrugated plates and flat plates restrained by a Winkler tensionless foundation and subjected to linearly varying in-plane loadings, where the corrugated plates are modelled as orthotropic plates and the flat plates are modelled as isotropic plates. The critical step in the presented method is the explicit expression for the lateral buckling mode function, which is derived through using the energy method. Simply supported and clamped edges conditions on the unloaded edges are considered in this study. The acquired lateral deflection function is applied to the governing buckling equations to eliminate the lateral variable. Considering the boundary conditions and continuity conditions at the border line between the contact and non-contact zones, the buckling coefficients and the corresponding buckling modes are found. The analytical solution to the buckling coefficients is also expressed through a fitted approximate formula in terms of foundation stiffness, which is verified through previous studies and finite element (FE) method.