• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.702-704
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• 2004

This paper focuses on the problem of asymptotic stabilization for uncertain time-delay systems with saturating actuator. We propose a state feedback controller which maximizes the delay bound for guaranteeing stability of the system. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. The criterion is represented in terms of LMIs, which can be solved by various efficient convex optimization algorithm. Numerical examples are given to illustrate our main method.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.4
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• pp.147-153
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• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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• pp.458-465
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• 2008

In this paper, we propose a non-fragile guaranteed cost controller design method for uncertain linear systems with constant delyas in state. The norm bounded and time-varying uncertainties are subjected to system and controller design matrices. A quadratic cost function is considered as the performance measure for the system. Based on the Lyapunov method, an LMI(Linear Matrix Inequality) optimization problem is established to design the controller which uses information of delayed state and minimizes the upper bound of the quadratic cost function for all admissible system uncertainties and controller gain variations. Numerical examples show the effectiveness of the proposed method.

• Proceedings of the KIPE Conference
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• 2001.10a
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• pp.276-280
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• 2001

In this paper, an approach to the design of negative impedance stabilizing controllers for PWM DC/DC converters that are used in DC switching. power supplies with constant power loads is presented. The control approach is based on the feedback linearization technique. Because of the negative impedance destabilizing characteristics of constant power loads, classical linear control methods have stability limitations around the operating points. However, the proposed stabilizing technique improves large-signal stability and dynamic responses. The proposed controllers are simulated and their responses under different operations are studied. Stability of the control technique is also verified using the second theorem of Lyapunov.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.110-113
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• 2003

In this paper, we propose that the chaotic behavior analysis in the mobile robot of embedding Arnold equation with obstacle. In order to analysis of chaotic behavior in the mobile robot, we apply not only qualitative analysis such as time-series, embedding phase plane, but also quantitative analysis such as Lyapunov exponent in the mobile robot with obstacle. In the obstacle, we only assume that all obstacles in the chaos trajectory surface in which robot workspace has an unstable limit cycle with Van der Pol equation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.141-144
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• 2003

A composite adaptive dual fuzzy controller combining the approximate mathematical model, linguistic model description, linguistic control rules and identification modeling error into a single adaptive fuzzy controller is developed for a nonlinear system. It ensures the system output tracks the desired reference value and excites the plant sufficiently for accelerating the parameter estimation process so that the control performances are greatly improved. Using the Lyapunov synthesis approach, proposed controller is analyzed and simulation results verify the effectiveness of the proposed control algorithm.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.5-8
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• 2003

In this paper, we propose that the chaotic behavior analysis in the mobile robot of embedding Chua's equation with obstacle. In order to analysis of chaotic behavior in the mobile robot, we apply not only qualitative analysis such as time-series, embedding phase plane, but also quantitative analysis such as Lyapunov exponent in the mobile robot with obstacle. In the obstacle, we only assume that all obstacles in the chaos trajectory surface in which robot workspace has an unstable limit cycle with Van der Pol equation

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1117-1127
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• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.2
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• pp.357-364
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• 2002

A new chattering free sliding made control is proposed for robot manipulators. The control input is derived from the reaching law and the Lyapunov stability criteria, which is only composed of continuous terms. It has a chattering free characteristics and a concise farm. In implementing procedures, no change of equations is needed. Thus, it does not degrade the original merits of the sliding mode control. And it is applied to a 2-link SCARA robot manipulator. It is shown that the proposed control has good trajectory tracking performance compared with the PD control and the conventional sliding mode control which uses the boundary layer concept.

• International Journal of Automotive Technology
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• v.8 no.4
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• pp.467-476
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• 2007

This work verifies the chaotic motion of a steer-by-wire vehicle dynamic system, and then elucidates an application of dither smoothing to control the chaos of a vehicle model. The largest Lyapunov exponent is estimated from the synchronization to identify periodic and chaotic motions. Then, a bifurcation diagram reveals complex nonlinear behaviors over a range of parameter values. Finally, a method for controlling a chaotic vehicle dynamic system is proposed. This method involves applying another external input, called a dither signal, to the system. The designed controller is demonstrated to work quite well for nonlinear systems in achieving robust stability and protecting the vehicle from slip or spin. Some simulation results are presented to establish the feasibility of the proposed method.