• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.787-797
• /
• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Journal of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.779-794
• /
• 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.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.64 no.6
• /
• pp.891-899
• /
• 2015

This paper presents the robust stability condition of uncertain Takagi-Sugeno(T-S) fuzzy systems with time-varying delay. New augmented Lyapunov-Krasovskii function is constructed to ensure that the system with time-varying delay is globally asymptotically stable. Also, less conservative delay-dependent stability criteria are obtained by employing some integral inequality, reciprocally convex approach and new delay-partitioning method. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.187-190
• /
• 1997

In the past few years, many researchers are interesting of control of mobile robot with nonholonomic constraints. And tracking problems is important as well as regulation in nonholonomic system control. Some researchers have investigated the stable tracking control law for mobile robot. But, few results showed the globally asymptotically stable control method simply. So, we address the design of globally asymptotically stable tracking control law for mobile robot with nonholonomic velocity constraints using simple method. The stabilizability of the controller is derived by Lyapunov direct method. And we analyze the system responses according to the variation of control parameters in line tracking problem. It is derived that the responses represent no overshoot property in line tracking. Examples are two-wheeled mobile robot and car-like mobile robot and the simulation results represent the effectiveness of our method.

• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.71-82
• /
• 2009

In this paper, a stage-structured predator-prey system with impulsive perturbations and time delays is presented to investigate the ecological problem of how a pest population and natural enemy population can coexist. Sufficient conditions are obtained using a discrete dynamical system determined by a stroboscopic map, which guarantee that a 'predator-extinction' periodic solution is globally attractive. When the impulsive period is longer than some time threshold or the impulsive harvesting rate is below a control threshold, the system is permanent. Our results provide some reasonable suggestions for pest management.

• Structural Engineering and Mechanics
• /
• v.56 no.3
• /
• pp.385-407
• /
• 2015

This paper deals with the problem of the global stabilization for a class of tension leg platform (TLP) nonlinear control systems. It is well known that, in general, the global asymptotic stability of the TLP subsystems does not imply the global asymptotic stability of the composite closed-loop system. Finding system parameters for stabilizing the control system is also an issue need to be concerned. In this paper, we give additional sufficient conditions for the global stabilization of a TLP nonlinear system. In particular, we consider a class of NN based Takagi-Sugeno (TS) fuzzy TLP systems. Using the so-called parallel distributed compensation (PDC) controller, we prove that this class of systems can be globally asymptotically stable. The proper design of system parameters are found by a swarm intelligence algorithm called Evolved Bat Algorithm (EBA). An illustrative example is given to show the applicability of the main result.

• Proceedings of the KIEE Conference
• /
• 2004.11c
• /
• pp.379-381
• /
• 2004

In this paper, a robust $H_{\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H_{\infty}$ controllers are given in terms of linear matrix inequalities.

• Proceedings of the KIEE Conference
• /
• 2005.07d
• /
• pp.2723-2725
• /
• 2005

In this paper, a robust $H{\infty}$ stabilization problem to a uncertain discrete-time nonlinear systems with time-delay via fuzzy static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-delayed state. Then parallel distributed compensation technique is used for designing of the robust fuzzy controller. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H{\infty}$ controllers are given in terms of linear matrix inequalities via similarity transform and congruence transform technique.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.1486-1491
• /
• 2005

In this paper, a robust H${\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent uncertain nonlinear systems with time-varying delayed state, which is a continuous-time or discrete-time system. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H${\infty}$controllers are given in terms of linear matrix inequalities.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2005.04a
• /
• pp.149-152
• /
• 2005

In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.