• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.271-274
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• 1995

This paper is concerned with the problem of robust stabilization of uncertain single-input and single-output nonlinear systems. Based on the input/output linearization approach for nonlinear state feedback synthesis in conjunction with Lyapunov methods, a stabilizing state feedback controller is proposed. Compared with the controllers reported in the control literature, instead of uniform ultimate boudedness, the controller proposed in this paper can guarantee uniform asymptotic stability of nonlinear systems in the presence of uncertainties. The required information about uncertain dynamics in the system is only that the uncertainties are bounded in Euclidean norm by known functions of the system state.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• The Journal of the Korea institute of electronic communication sciences
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• v.1 no.1
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• pp.49-55
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• 2006

Applied by periodic Stimulating Currents in Bonhoeffer -Van der Pol(BVP) model, chaotic and periodic phenomena occured at specific conditions. The conditions of the chaotic motion in BVP comprised 0.7182< $A_1$ <0.792 and 1.09< $A_1$ <1.302 proved by the analysis of phase plane, bifurcation diagram, and lyapunov exponent. To control the chaotic motion, two methods were suggested by the first used the amplitude parameter A1, $A1={\varepsilon}((x-x_s)-(y-y_s))$ and the second used the temperature parameterc, $c=c(1+{\eta}cos{\Omega}t)$ which the values of ${\eta},{\Omega}$ varied respectlvly, and $x_s$, $y_s$ are the periodic signal. As a result of simulating these methods, the chaotic phenomena was controlled with the periodic motion of periodisity. The feasibilities of the chaotic and the periodic phenomena were analysed by phase plane Poincare map and lyapunov exponent.

• Journal of Power Electronics
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• v.19 no.1
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• pp.89-98
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• 2019

This paper analyzes the input side performance of a conventional three-phase to single-phase matrix converter (3-1MC). It also presents the input-side waveform quality under this topology. The suppression of low-frequency input current harmonics is studied using the 3-1MC plus capacitance compensation unit. The constraint between the modulation function of the output and compensation sides is analyzed, and the relations among the voltage utilization ratio and the output compensation capacitance, filter capacitors and other system parameters are deduced. For a 3-1MC without large-capacity energy storage, the system performance is susceptible to input voltage imbalance. This paper decouples the inner current of the 3-1MC using a Lyapunov function in the input positive and negative sequence bi-coordinate axes. Meanwhile, the outer loop adopts a voltage-weighted synthesis of the output and compensation sides as a cascade of control objects. Experiments show that this strategy suppresses the low-frequency input current harmonics caused by input voltage imbalance, and ensures that the system maintains good static and dynamic performances under input-unbalanced conditions. At the same time, the parameter selection and debugging methods are simple.

• East Asian mathematical journal
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• v.24 no.1
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• pp.57-65
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• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.263-284
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• 2012

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

• International Journal of Automotive Technology
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• v.1 no.1
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• pp.48-55
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• 2000

Two major roles of the traction control system (TCS) are to guarantee the acceleration performance and directional stability even in extreme road conditions, under which average drivers may not control the car properly. Commercial TCSs use experiential methods such as lookup table and gain-scheduling to achieve proper performance under various road and vehicle conditions. This paper proposes a new slip controller which uses the brake and the throttle actuator simultaneously. To avoid measurement problems and to get a simple structure, the brake controller and the throttle controller are designed using Lyapunov redesign method and multiple sliding mode control respectively. Through the hybrid use of brake and throttle controllers, the vehicle is insensitive to the variation of the vehicle mass, brake gain and road condition and can achieve the required acceleration performance. The proposed method is validated with simulations based on 15 DOF passenger car model.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.594-600
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• 2007

A sufficient condition for the robust D-stability of dynamic interval systems is proposed in this paper. This D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of matrix inequalities defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as previous results. This condition is also extended to the robust D-stabilization problem of dynamic interval systems, which supplies an effective synthesis procedure for any LMI D-region. The proposed conditions can be simplified to a set of LMIs, which can be solved by efficient interior point methods in polynomial time.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.401-406
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• 2012

This paper considers multi-agent systems with interval time-varying delays and switching interconnection topology. By construction of a suitable Lyapunov-Krasovskii's functional, new delay-dependent consensus control conditions for the systems are established in terms of LMIs (Linear Matrix Inequalities) which can be easily solved by various effective optimization algorithms. One numerical example is given to illustrate the effectiveness of the proposed methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.376-382
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• 2011

This paper proposes delay-dependent stability conditions of the fuzzy Markovian jumping Hopfield neural networks of neutral type with time-varying delays. By constructing a suitable Lyapunov-Krasovskii's (L-K) functional and utilizing Finsler's lemma, new delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed methods.