• Title/Summary/Keyword: Lyapunov stability criterion

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A New Augmented Lyapunov Functional Approach to Robust Delay-dependent Stability Analysis for Neutral Time-delay Systems (뉴트럴 시간지연 시스템의 강인 지연의존 안정성 해석을 위한 새로운 리아프노프 함수법)

  • Kwon, Oh-Min
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.3
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    • pp.620-624
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    • 2011
  • This paper propose a new delay-dependent stability criterion of neutral time-delay systems. By employing double-integral terms in augmented states and constructing a new Lyapunov-Krasovskii's functional, a delay-dependent stability criterion is established in terms of Linear Matrix Inequality. Through numerical examples, the validity and improvement results obtained by applying the proposed stability criterion will be shown.

Stability of Switched Linear Systems Using Upper Bounds of Solutions of Lyapunov Matrix Equations (리야프노프 행렬 방정식의 해를 이용한 스위칭 선형시스템의 안정화)

  • Yeom, Dang-Hae;Choi, Jin-Young
    • Proceedings of the KIEE Conference
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    • 2005.10b
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    • pp.20-22
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    • 2005
  • In this paper, we propose a novel stability criterion for switched linear systems. The proposed method employs the results on the upper bound of the solution of LME(Lyapunov Matrix Equation) and on the stability of hybrid system. The former guarantees the existence of Lyapunov-like energy functions and the latter shows that the stability of switched linear systems by using these energy functions. The proposed criterion releases the restriction on the stability of switched linear systems comparing with the existing methods and provides us with easy implementation way for pole assignment.

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Robust Delay-dependent Stability Criterion for Uncertain Networked Control System (불확실성이 존재하는 네트워크 제어시스템의 강인 지연의존 안정성 판별법)

  • Park, Myeongjin;Kwon, Ohmin;Park, Ju H.
    • IEMEK Journal of Embedded Systems and Applications
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    • v.4 no.2
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    • pp.97-102
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    • 2009
  • In this paper, the problem of stability analysis for networked control systems with norm-bounded parameter uncertainties is investigated. By construction Lyapunov's functional, a new delay-dependent stability criterion for uncertain networked control system is established in terms of LMIs (linear matrix inequalities) which can be easily by various convex optimization algorithms. One numerical example is included to show the effectiveness of proposed criterion.

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Stabilization of Switched Linear Systems (선형 스위칭 시스템의 안정화)

  • Yeom, Dong-Hae;Im, Ki-Hong;Choi, Jin-Young
    • Proceedings of the KIEE Conference
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    • 2004.05a
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    • pp.13-15
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    • 2004
  • In this paper, we propose a novel stability criterion and a guideline of controller design for switched linear systems. Unlike existing criterions such as Lie algebraic method and multiple Lyapunov functions method, the proposed criterion can be applied to each individual system without considering an overall system. By applying the proposed criterion to each individual system separately, a state feedback controller can be easily designed. Stability of the overall system is proved by developing a rule to determine non-increasing Lyapunov functions recursively at each switching instant. An illustrative example is given.

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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.

New Delay-dependent Stability Criterion for Neural Networks with Discrete and Distributed Time-varying Delays (이산 및 분산 시변 지연을 가진 뉴럴 네트워크에 대한 새로운 시간지연 종속 안정성 판별법)

  • Park, Myeong-Jin;Kwon, Oh-Min;Park, Ju-Hyun;Lee, Sang-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.58 no.9
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    • pp.1809-1814
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    • 2009
  • In this paper, the problem of stability analysis for neural networks with discrete and distributed time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical example are included to show the effectiveness of proposed criterion.

Delay-dependent Robust Stability of Uncertain Dynamic Systems with Time-varying Delays (시변 지연이 존재하는 불확실 동적 시스템의 지연 의존 강인 안정성)

  • Kwon, Oh-Min;Park, Ju-Hyun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.58 no.1
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    • pp.181-186
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    • 2009
  • In this paper, the stability analysis for uncertain dynamic systems with time-varying delays is considered. By constructing a new Lyapunov functional, a novel stability criterion is established in terms of linear matrix inequalities (LMIs). Two numerical examples are carried out to support the effectiveness of the proposed method.

On Delay-Dependent Stability of Neutral Systems with Mixed Time-Varying Delay Arguments

  • Park, H.J.
    • KIEE International Transaction on Systems and Control
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    • v.12D no.1
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    • pp.39-42
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    • 2002
  • This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.

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Active TMD systematic design of fuzzy control and the application in high-rise buildings

  • Chen, Z.Y.;Jiang, Rong;Wang, Ruei-Yuan;Chen, Timothy
    • Earthquakes and Structures
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    • v.21 no.6
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    • pp.577-585
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    • 2021
  • In this research, a neural network (NN) method was developed, which combines H-infinity and fuzzy control for the purpose of stabilization and stability analysis of nonlinear systems. The H-infinity criterion is derived from the Lyapunov fuzzy method, and it is defined as a fuzzy combination of quadratic Lyapunov functions. Based on the stability criterion, the nonlinear system is guaranteed to be stable, so it is transformed to be a linear matrix inequality (LMI) problem. Since the demo active vibration control system to the tuning of the algorithm sequence developed a controller in a manner, it could effectively improve the control performance, by reducing the wind's excitation configuration in response to increase in the cost efficiency, and the control actuator.

State-Space Analysis on The Stability of Limit Cycle Predicted by Harmonic Balance

  • Lee, Byung-Jin;Yun, Suk-Chang;Kim, Chang-Joo;Park, Jung-Keun;Sung, Sang-Kyung
    • Journal of Electrical Engineering and Technology
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    • v.6 no.5
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    • pp.697-705
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    • 2011
  • In this paper, a closed-loop system constructed with a linear plant and nonlinearity in the feedback connection is considered to argue against its planar orbital stability. Through a state space approach, a main result that presents a sufficient stability criterion of the limit cycle predicted by solving the harmonic balance equation is given. Preliminarily, the harmonic balance of the nonlinear feedback loop is assumed to have a solution that determines the characteristics of the limit cycle. Using a state-space approach, the nonlinear loop equation is reformulated into a linear perturbed model through the introduction of a residual operator. By considering a series of transformations, such as a modified eigenstructure decomposition, periodic averaging, change of variables, and coordinate transformation, the stability of the limit cycle can be simply tested via a scalar function and matrix. Finally, the stability criterion is addressed by constructing a composite Lyapunov function of the transformed system.