• Title, Summary, Keyword: global stability

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GLOBAL STABILITY OF VIRUS DYNAMICS MODEL WITH IMMUNE RESPONSE, CELLULAR INFECTION AND HOLLING TYPE-II

  • ELAIW, A.M.;GHALEB, SH.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.1
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    • pp.39-63
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    • 2019
  • In this paper, we study the effect of Cytotoxic T Lymphocyte (CTL) and antibody immune responses on the virus dynamics with both virus-to-cell and cell-to-cell transmissions. The infection rate is given by Holling type-II. We first show that the model is biologically acceptable by showing that the solutions of the model are nonnegative and bounded. We find the equilibria of the model and investigate their global stability analysis. We derive five threshold parameters which fully determine the existence and stability of the five equilibria of the model. The global stability of all equilibria of the model is proven using Lyapunov method and applying LaSalle's invariance principle. To support our theoretical results we have performed some numerical simulations for the model. The results show the CTL and antibody immune response can control the disease progression.

GLOBAL STABILITY ANALYSIS FOR A CLASS OF COHEN-GROSSBERG NEURAL NETWORK MODELS

  • Guo, Yingxin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1193-1198
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    • 2012
  • By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

A Stability Analysis Scheme for a Class of First-Order Nonlinear Time-Delay Systems (일종의 일차 비선형 시간 지연 시스템을 위한 안정성 분석 방법)

  • Choi, Joon-Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.6
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    • pp.554-557
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    • 2008
  • We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

Uniform ultimate boundedness of control systems with matched and mismatched uncertainties by Lyapunov-like method

  • Sung, Yulwan;Shibata, Hiroshi;Park, Chang-Young;Kwo, Oh-Kyu
    • 제어로봇시스템학회:학술대회논문집
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    • pp.119-122
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    • 1996
  • The recently proposed control method using a Lyapunov-like function can give global asymptotic stability to a system with mismatched uncertainties if the uncertainties are bounded by a known function and the uncontrolled system is locally and asymptotically stable. In this paper, we modify the method so that it can be applied to a system not satisfying the latter condition without deteriorating qualitative performance. The assured stability in this case is uniform ultimate boundedness which is as useful as global asymptotic stability in the sense that it is global and the bound can be taken arbitrarily small. By the proposed control law we can deal with both matched and mismatched uncertain systems. The above facts conclude that Lyapunov-like control method is superior to any other Lyapunov direct methods in its applicability to uncertain systems.

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Stabilization of nonlinear systems using compensated fuzzy controllers (보상 퍼지 제어기를 이용한 비선형 시스템의 안정화)

  • 강성훈;박주영
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.34C no.5
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    • pp.43-54
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    • 1997
  • The objective of this paper is to present a controller-design method that can guarantee the global stability for nonlinear systems described by takagi-sugeno fuzzy models, and to apply the method to a typical nonlinear control problem. The presented method gives us a compensated fuzzy controller through the following major steps: First, if each local linear model of a given takagi-sugeno fuzzy system does not have the same input matrix, the method expands the system into the one with a method finds a takagi-sugeno fuzzy controller guaranteeing the global stability of the closed loop via solving relevant linear matrix inequalities. Compared to the conventional PDC (paralled distributed compensation) technique, the presented method has an advantage that trial-and-errors to check the global stability are not necessary. An illustrative simulation on the control of inverted pendulum is performed to demonstrate the applicability of the presented method, and its results show that a controller satisfying the global stability and robustness can be obtained by the method.

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DELAY-DEPENDENT GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED CELLULAR NEURAL NETWORKS

  • Yang, Yitao;Zhang, Yuejin
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.583-596
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    • 2010
  • In this paper, the problem of delay-dependent stability analysis for cellular neural networks systems with time-varying delays was considered. By using a new Lyapunov-Krasovskii function, delay-dependant stability conditions of the delayed cellular neural networks systems are proposed in terms of linear matrix inequalities (LMIs). Examples are provided to demonstrate the reduced conservatism of the proposed stability results.

GLOBAL ANALYSIS FOR A DELAY-DISTRIBUTED VIRAL INFECTION MODEL WITH ANTIBODIES AND GENERAL NONLINEAR INCIDENCE RATE

  • Elaiw, A.M.;Alshamrani, N.H.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.18 no.4
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    • pp.317-335
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    • 2014
  • In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

GLOBAL ROBUST STABILITY OF TIME-DELAY SYSTEMS WITH DISCONTINUOUS ACTIVATION FUNCTIONS UNDER POLYTOPIC PARAMETER UNCERTAINTIES

  • Wang, Zengyun;Huang, Lihong;Zuo, Yi;Zhang, Lingling
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.89-102
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    • 2010
  • This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration (계단식 블록식 보강토 옹벽의 전체 안전성)

  • Yoo, Chung-Sik;Kim, Sun-Bin
    • Journal of the Korean Geotechnical Society
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    • v.24 no.9
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    • pp.23-32
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    • 2008
  • This paper presents the global stability of geosynthetic reinforced segmental retaining walls in tiered configuration. Four design cases of walls with different geometries and offset distances were analyzed based on the FHWA and NCMA design guidelines and the discrepancies between the different guidelines were identified. A series of global slope stability analyses were conducted using the limit-equilibrium analysis and the continuum mechanics based shear strength reduction method with the aim of identifying failure patterns and the associated factors of safety. The results indicated among other things that the FHWA design approach yields conservative results both in the external and internal stability calculations, i.e., lower factors of safety, than the NCMA design approach. It was also found that required reinforcement lengths are usually governed by the global slope stability requirement rather than the external stability calculations. Also shown is that the required reinforcement lengths for the upper tiers are much longer than those based on the current design guidelines.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF PERIODIC SOLUTIONS TO A FRACTIONAL CHEMOTAXIS SYSTEM ON THE WEAKLY COMPETITIVE CASE

  • Lei, Yuzhu;Liu, Zuhan;Zhou, Ling
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1269-1297
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    • 2020
  • In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p0, where p0 is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.