• Korean Journal of Mathematics
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• v.30 no.2
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• pp.205-229
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• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1017-1035
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• 2023

In this paper, we construct a monkeypox model which is similar to smallpox infection. It is caused by a monkeypox virus which is related to Poxviridae family. It will occur mostly in West African communities and in remote Central. We develop a system of differential equations for an SEIR (Suspected, Exposed, Infected and Recovered) model and analyze the outbreak of monkeypox disease and its effect on United States(US) population. We establish theorems on asymptotical stability conditions for endemic equilibrium and disease-free equilibrium. The basic reproduction number R₀ has been determined using next generation matrix. We expect that this study will be effective at controlling monkeypox spread in United States. Our goal is to see whether monkeypox can be controlled and destroyed by smallpox vaccination. We find that monkeypox is controllable and can be fully destroyed in disease free state by vaccination. However, in the endemic state, monkeypox cannot be destroyed by vaccination alone.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.58-69
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• 1996

This paper presents a new approach to derive an energy integral based on an Equivalent Mechanical Model(EMM), which is developed by introducing imaginary springs for line resistances. The proposed EMM shows that phasor currents and voltages are directly analogous to the two-dimensional force and displacement vectors, respectively. Through rigorous energy analysis of the proposed EMM, an exact energy integral expression is derived for multimachine systems, and several useful theorems are developed to derive an energy integral for power systems with detailed generator models the energy integral exactly reflects the internal resistance, saliency and flux-decaying effects of the generator. Finally, an illustrative example is given for a multimachine system adopting the Eq'-model for generators, which shows that the consideration of a detailed generator model does not aggravate the complicacy of the direct method of stability analysis in multimachine systems.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.5
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• pp.18-29
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• 2007

The main objective of this paper is to propose a new stability analysis method for a networked control system with multiple packet transmission. The new scheduling method that can guarantee the maximum time delay and discrete switch state equation model which represent a network data loss is proposed. The equivalent model of a MIMO(multi-input multi-output) networked control system is derived from a state space model of linear time invariant interconnected systems in the form of asynchronous dynamical system. Using this model, this paper presents new stability theorems that can determine stability of the networked control system with regard to time delay, data loss, and the number of transmission packets. Simulation results verify the effectiveness of proposed stability analysis method.

• Earthquakes and Structures
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• v.17 no.3
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• pp.307-315
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• 2019

Building prediction and control theory have been drawing the attention of many scientists over the past few years because design and control efficiency consumes the most financial and energy. In the literature, many methods have been proposed to achieve this goal by trying different control theorems, but all of these methods face some problems in correctly solving the problem. The Evolutionary Bat (EB) Algorithm is one of the recently introduced optimization methods and providing researchers to solve different types of optimization problems. This paper applies EB to the optimization of building control design. The optimized parameter is the input to the fuzzy controller, which gives the status response as an output, which in turn changes the state of the associated actuator. The novel control criterion for guarantee of the stability of the system is also derived for the demonstration in the analysis. This systematic and simplified controller design approach is the contribution for solving complex dynamic engineering system subjected to external disturbances. The experimental results show that the method achieves effective results in the design of closed-loop system. Therefore, by establishing the stability of the closed-loop system, the behavior of the closed-loop building system can be precisely predicted and stabilized.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.586-592
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• 1999

We investigate the characteristic of 소데 responses of the Manabe standard form which is used recently for design of the controller. We obtain some theorems and these theorems have the properties of the relationship between the roots of the polynomial and the stability indices which are used for the Manabe standard form. The Manabe standard form has the following properties: The sum of the squal to zero, the sum of the reciprocal of the squared roots is greater than zero and the parameter $\tau$ is the negative value of the sum of the reciprocal of the roots. We compare the step responses of the Manabe standard form with those of the ITAE form, the dead beat response and Bessel forms. We choose the 6th order closed loop polynomial and keep the same settling time for the four forms. Under these conditions we find that the Manabe standard form have faster 90% rising time than the Bessel and dead beat response. We see that the ITAE, bessel and dead beat responses have some overshoot, whereas the Manabe standard form has none. We also compare the Manabe form with the other three forms for the controller design using the pole assignment technique. If the open loop transfer function is a type-1 system (transfer functions having one integrator), then, for the closed loop system associated with the open loop transfer function, the steady state error of the unit ramp input is obtained in terms of the parameter $\tau$ of the Manabe standard form.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.10
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• pp.1894-1899
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• 2010

This note is concerned with a robust sliding mode control(SMC) for a class of unmatched uncertain system with severe commensurate state time delay. The suggested method is extended to the control of severe state time delay systems with unmatched uncertainties except the matched input matrix uncertainty. A transformed sliding surface is proposed and a stabilizing control input is suggested. The closed loop stability together with the existence condition of the sliding mode on the proposed sliding surface is investigated through one Lemma and two Theorems by using the Lyapunov direct method with the concept of the control Lyapunov function instead of complex Lyapunov-Kravoskii functionals. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.