• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.29-62
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• 2018

We investigate a class of HIV infection models with two kinds of target cells: $CD4^+$ T cells and macrophages. We incorporate three distributed time delays into the models. Moreover, we consider the effect of humoral immunity on the dynamical behavior of the HIV. The viruses are produced from four types of infected cells: short-lived infected $CD4^+$T cells, long-lived chronically infected $CD4^+$T cells, short-lived infected macrophages and long-lived chronically infected macrophages. The drug efficacy is assumed to be different for the two types of target cells. The HIV-target incidence rate is given by bilinear and saturation functional response while, for the third model, both HIV-target incidence rate and neutralization rate of viruses are given by nonlinear general functions. We show that the solutions of the proposed models are nonnegative and ultimately bounded. We derive two threshold parameters which fully determine the positivity and stability of the three steady states of the models. Using Lyapunov functionals, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

• 대한수학회지
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• 제49권4호
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• 대한수학회보
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• 제54권6호
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• pp.1893-1912
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• 2017

In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.

• 대한임베디드공학회논문지
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• 제15권3호
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• pp.139-148
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• 2020

This paper is concerned with the H₂ attitude controller design for 3 degree of freedom (DOF) Hover systems with an event-triggered mechanism. The 3 DOF Hover system is an embedded platform for unmanned aerial vehicle (UAV) provided by Quanser. The mathematical model of this system is obtained by a linearization around operating points and it is represented as a linear parameter-varying (LPV) model. To save communication network resources, the event-triggered mechanism (ETM) is considered and the performance of the system is guaranteed by the H₂ controller. The stabilization condition is obtained by using Lyapunov-Krasovskii functionals (LKFs) and some useful lemmas. The effectiveness of the proposed method is shown by simulation and experimental results.

• International Journal of Control, Automation, and Systems
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• 제6권1호
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• pp.15-23
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• 2008

This paper considers the problem of delay-dependent guaranteed cost controller design for uncertain neutral systems with distributed delays. The system under consideration is subject to norm-bounded time-varying parametric uncertainty appearing in all the matrices of the state-space model. By constructing appropriate Lyapunov functionals and using matrix inequality techniques, a state feedback controller is designed such that the resulting closed-loop system is not only robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. Furthermore, a convex optimization problem is introduced to minimize a specified cost bound. By matrix transformation techniques, the corresponding optimal guaranteed controller can be obtained by solving a linear matrix inequality. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed approach.

• 대한임베디드공학회논문지
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• 제14권5호
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• pp.269-275
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• 2019

This paper addresses the control problem of cyber-physical systems under controller attack. A novel discontinuous Lyapunov functionals are employed to fully utilize sampled-data pattern which characteristic is commonly appeared in cyber-physical systems. By considering the limited resource of networks, cyber-attacks on the controller are considered randomly occurring and are described as an attack function which is nonlinear but assumed to be satisfying Lipschitz condition. Novel criteria for designing controller with robustness for cyber-attacks are developed in terms of linear matrix inequality (LMI). Finally, a numerical example is given to prove the usefulness of the proposed method.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.629-648
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• 2021

In this paper, we study a within-host mathematical model of HCV infection and carry out mathematical analysis of the global dynamics and bifurcations of the model in different parameter regimes. We explore the effect of reverse transcriptase inhibitors (RTI) on spontaneous HCV clearance. The model can produce all clinically observed patient profiles for realistic parameter values; it can also be used to estimate the efficacy and/or duration of treatment that will ensure permanent cure for a particular patient. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

• 한국지능시스템학회논문지
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• 제20권2호
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• pp.159-164
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• 2010

본 논문에서는 뉴트럴 타입 시간 지연을 갖는 네트워크 제어 시스템의 안정도 분석 및 제어기 설계에 대해서 논의한다. 네트워크상에서 발생하는 뉴트럴 타입 시간 지연을 모델링하며, 전체 네트워크 제어 시스템은 뉴트럴 타입 시간 지연을 가지는 비선형 시스템이 된다. 시간 지연 분산 방법을 이용하여 기존과 다른 새로운 안정도 조건을 유도한다. 리아프노푸 함수를 이용하여 제안된 네트워크 제어 시스템을 안정화 시키는 퍼지 제어기 설계를 위한 충분조건을 유도한다. 제안된 충분조건을 선형 행렬 부등식의 형태로 나타내고, 해를 통하여 퍼지 제어기의 이득 값을 설계한다. 예제를 통하여 제안된 이론의 타당성을 확인한다.

• 한국지능시스템학회논문지
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• 제22권2호
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• pp.174-180
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• 2012

본 논문은 미지의 시간 지연을 갖는 비선형 상호 연결 시스템을 위한 분산 적응 출력 궤환 제어기를 제안한다. 미지의 시간 지연을 갖는 상호 연결 부분은 부시스템들의 모든 상태 변수를 포함한다. 적당한 르아브노브-크라소브스키 함수와 함수 예측 기법을 사용하여 시간 지연 함수들을 보상한다. 각각의 부시스템을 위한 시간에 독립적인 지역 제어기를 설계하기 위해 관측 동적 표면 제어 기법을 이용한다. 제어된 페루프 시스템의 모든 신호들이 준 전역적이고 균일하게 유계됨과 제어 오차가 원점 주위의 조절 가능한 주변으로 수렴함을 증명한다.