• Title, Summary, Keyword: global stability

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A Globally Stabilizing Model Predictive Controller for Neutrally Stable Linear Systems with Input Constraints

  • Yoon, Tae-Woong;Kim, Jung-Su;Jadbabaie, Ali;Persis, Claudio De
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1901-1904
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    • 2003
  • MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

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GLOBAL ASYMPTOTIC STABILITY OF A SECOND ORDER RATIONAL DIFFERENCE EQUATION

  • Abo-Zeid, R.
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.797-804
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    • 2010
  • The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS

  • Quyet, Dao Trong
    • Communications of the Korean Mathematical Society
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    • v.29 no.4
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    • pp.505-518
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    • 2014
  • Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

GLOBAL ATTRACTOR FOR A SEMILINEAR PSEUDOPARABOLIC EQUATION WITH INFINITE DELAY

  • Thanh, Dang Thi Phuong
    • Communications of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.579-600
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    • 2017
  • In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

GLOBAL STABILITY OF HIV INFECTION MODELS WITH INTRACELLULAR DELAYS

  • Elaiw, Ahmed;Hassanien, Ismail;Azoz, Shimaa
    • Journal of the Korean Mathematical Society
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    • v.49 no.4
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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.

ON GLOBAL EXPONENTIAL STABILITY FOR CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Kwon, O.M.;Park, Ju-H.;Lee, S.M.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.961-972
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    • 2008
  • In this paper, we consider the global exponential stability of cellular neural networks with time-varying delays. Based on the Lyapunov function method and convex optimization approach, a novel delay-dependent criterion of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, the interior point algorithm is utilized in this work. Two numerical examples are given to show the effectiveness of our results.

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GLOBAL ASYMPTOTIC STABILITY FOR A DIFFUSION LOTKA-VOLTERRA COMPETITION SYSTEM WITH TIME DELAYS

  • Zhang, Jia-Fang;Zhang, Ping-An
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1255-1262
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    • 2012
  • A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

STABILITY OF IMPULSIVE CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Lijuan;Yu, Lixin
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1327-1335
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    • 2011
  • This paper demonstrates that there is a unique exponentially stable equilibrium state of a class of impulsive cellular neural network with delays. The analysis exploits M-matrix theory and generalized comparison principle to derive some easily verifiable sufficient conditions for the global exponential stability of the equilibrium state. The results extend and improve earlier publications. An example with its simulation is given for illustration of theoretical results.

EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITHOUT GLOBAL LIPSCHITZ CONDITIONS

  • Liu, Bingwan
    • Journal of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.873-887
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    • 2007
  • In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

GLOBAL STABILITY OF THE POSITIVE EQUILIBRIUM OF A MATHEMATICAL MODEL FOR UNSTIRRED MEMBRANE REACTORS

  • Song, Yongli;Zhang, Tonghua
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.383-389
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    • 2017
  • This paper devotes to the study of a diffusive model for unstirred membrane reactors with maintenance energy subject to a homogeneous Neumann boundary condition. It shows that the unique constant steady state is globally asymptotically stable when it exists. This result further implies the non-existence of the non-uniform steady state solution.