• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.593-596
• /
• 2009

In this short note, we explicate a relation among Collet-Eckmann attractors, Lyapunov attractors and asymptotically stable attractors in the sense of J. Milnor[4].

• Proceedings of the KIPE Conference
• /
• 1997.07a
• /
• pp.97-100
• /
• 1997

A new control method for the robust position control of a brushless DC(BLDC) motor using the asymptotically stable adaptive load torque observer is presented. A precision position control is obtained for the BLDC motor system approximately linearized using the field-orientation method. And the application of the load torque observer is published in [1] using fixed gain. However, the flux linkage is not exactly known for a load torque observer. Therefore, a model reference adaptive observer is considered to overcome the problem of the unknown parameter in this paper. And stability analysis is carried out using Liapunov stability theorem. As a result, asymptotically stable observer gain can be obtained without affecting the overall system response. The load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent current having the fast response.

• The Pure and Applied Mathematics
• /
• v.7 no.2
• /
• pp.129-135
• /
• 2000

We show that a compact subset M of X is asymptotically stable if and only if a strict Lyapunov function of M exists.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.453-459
• /
• 2019

In this paper, we analyze the behaviour of flows near closed sets with compact boundary which contains no semi-orbits. Also, we give a condition that a closed invariant set is to be asymptotically stable.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.829-840
• /
• 2001

Generally it is not easy task whether the stable systems governed by nonlinear ordinary differential equations are asymptotically stable or not. This problem often appears in studying a collision and avoidance control problem based on the stability theory. In this paper we devoted to finding conditions that the stable system obtained from the collision and avoidance control problem is asymptotically stable.

• 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 applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1117-1127
• /
• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.1071-1086
• /
• 2005

In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4$^{+}$ T-cells, and the emission of viral particles on a cellular level. We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.455-469
• /
• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.1770-1773
• /
• 1997

In this paper, a linear discrete time system subject to the input saturatioin is shown to be exponentially stabilizable on any compact subset of the constrained asymptotically stabilizable set by a linear periodic variable structure controller. We also establish tat any neutrally stable system subject to the input saturation can be globally asymptotically stabilizable via linear feedback.