• Title/Summary/Keyword: lyapunov stability

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GLOBAL STABILITY ANALYSIS FOR A CLASS OF COHEN-GROSSBERG NEURAL NETWORK MODELS

  • Guo, Yingxin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1193-1198
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    • 2012
  • By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

A New Stability Criterion of a Class of Neutral Differential Equations (뉴트럴 미분방정식의 새로운 안정성 판별법)

  • Kwon, Oh-Min;Park, Ju-Hyun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.56 no.11
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    • pp.2023-2026
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    • 2007
  • In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

Stability Proof of NFL-FOO/SMC : Part 1 (NFL-FOO/SMC의 안정도 증명 : Part 1)

  • Lee, Sang-Seung;Park, Jong-Keun;Lee, Ju-Jang
    • Proceedings of the KIEE Conference
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    • 1998.07c
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    • pp.973-975
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    • 1998
  • For a nonlinear feedback linearization-full order observer/sliding mode controller (NFL-FOO/SMC), the separation principle is derived, and the closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

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The Interpretation Stability Uncertain Bound for the Uncertain Linear Systems via Lyapunov Equations (Lyapunov 방정식을 이용한 불확실한 선형 시스템의 안정한 섭동 유계 해석)

  • Cho, Do-Hyeoun;Lee, Sang-Hun;Lee, Jong-Yong
    • 전자공학회논문지 IE
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    • v.44 no.4
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    • pp.26-29
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    • 2007
  • In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the matrix Riccati equation.

On the Stability of Critical Point for Positive Systems and Its Applications to Biological Systems

  • Lee, Joo-Won;Jo, Nam Hoon;Shim, Hyungbo;Son, Young Ik
    • Journal of Electrical Engineering and Technology
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    • v.8 no.6
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    • pp.1530-1541
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    • 2013
  • The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

Implementation of a Lyapunov Function Based Fuzzy Controller for the Precise Positioning of DC Servo Motor

  • Lee, Joon-Tark;Lee, Oh-Keol;Shin, Song-Ho;Park, Doo-Hwan
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1998.06a
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    • pp.42-45
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    • 1998
  • In this paper, a fuzzy control technique using adjustable scale factors and Lyapunov Function for the precise position control of DC servo system is introduced. The suitable scale factors were selected and the stable control input using the stability theory of Lyapunov function cam be applied. Therefore, the controlled system have the robustness against disturbances and can be stabilized because of reinforced adaptivity. This proposed fuzzy controller is implemented on a 80586 micro-computer which have of fuzzy inference routine part, manipulating part of scale factors and DT-2801 data aquisition board.

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A V-Shaped Lyapunov Function Approach to Model-Based Control of Flexible-Joint Robots

  • Lee, Ho-Hoon;Park, Seung-Gap
    • Journal of Mechanical Science and Technology
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    • v.14 no.11
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    • pp.1225-1231
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    • 2000
  • This paper proposes a V-shaped Lyapunov function approach for the model-based control of flexible-joint robots, in which a new model-based nonlinear control scheme is designed based on a V-shaped Lyapunov function. The proposed control guarantees global asymptotic stability for link trajectory control while keeping all internal signals bounded. Since joint flexibility is used as a control parameter, the proposed control is not restricted by the degree of joint flexibility and be applied to flexibility-joint, partly-flexibility, or rigid-joint robots without modification. the effectiveness of the proposed control has been by computer simulation.

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Design of Lyapunov Theory based State Feedback Controller for Time-Delay Systems (시간지연 시스템을 위한 리아푸노브 이론 기반 상태 피드백 제어기 설계)

  • Cho, Hyun Cheol;Shin, Chan Bai
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.1
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    • pp.95-100
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    • 2013
  • This paper presents a new state feedback control approach for communication networks based control systems in which control input and output observation time-delay natures are generally occurred in practice. We first establish a generic state feedback control framework based on well-known linear system theory. A maximum time-delay value which allows critical stability of whole control system are defined to make a positive definite Lyapunov function which is mathematically composed of controlled system states. We analytically derive its control parameters by using a steepest descent optimization method in order to guarantee a stability condition through Lyapunov theory. Computer simulation is numerically carried out for demonstrating reliability of the proposed NCS algorithm and a comparative study is accomplished to prove its superiority for which the traditional control approach for NCS is made use of under same simulation scenarios.

Improvement of the Robustness Bounds of the Linear Systems with Structured Uncertainties (구조화된 불확실성의 비선형요소를 갖는 선형 시스템의 강인영역 개선)

  • Jo, Jang-Hyen
    • Journal of the Korean Society for Precision Engineering
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    • v.18 no.1
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    • pp.171-179
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    • 2001
  • The purpose of this paper is the derivation and development of the new definitions and methods for the new estimation of robustness for the systems having structured uncertainties. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. The systems considered are assumed to be nominally linear, with time-variant, nonlinear bounded perturbations. This new techniques demonstrate the improvement of robustness bounds from the numerical results.

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A Line-integral Fuzzy Lyapunov Functional Approach to Sampled-data Tracking Control of Takagi-Sugeno Fuzzy Systems

  • Kim, Han Sol;Joo, Young Hoon
    • Journal of Electrical Engineering and Technology
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    • v.13 no.6
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    • pp.2521-2529
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    • 2018
  • This paper deals with a sampled-data tracking control problem for the Takagi-Sugeno fuzzy system with external disturbances. We derive a stability condition guaranteeing both asymptotic stability and H-infinity tracking performance by employing a newly proposed time-dependent line-integral fuzzy Lyapunov-Krasovskii functional. A new integral inequality is also introduced, by which the proposed stability condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed method is demonstrated through a simulation example.