• Title, Summary, Keyword: Lyapunov functional

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Periodic Properties of a Lyapunov Functional of State Delay Systems

  • Young Soo Suh
    • KIEE International Transaction on Systems and Control
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    • v.2D no.2
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    • pp.92-96
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    • 2002
  • This paper is concerned with properties of a Lyapunov functional of state delay systems. It is shown that if a state delay system has a pure imaginary pole for some state delay, then no Lyapunov functional satisfying a Lyapunov condition exists periodically with respect to change of the state delay. This periodic property is unique in state delay systems and has been well known in the frequency domain stability conditions. However, in the time domain stability conditions using a Lyapunov functional, the periodic property is not known explicitly.

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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.

INSTABILITY OF SOLUTIONS FOR NONLINEAR DIFFERENTIAL EQUATIONS OF EIGHTH ORDER WITH MULTIPLE DEVIATING ARGUMENTS

  • Tunc, Cemil
    • Journal of applied mathematics & informatics
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    • v.30 no.5_6
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    • pp.741-748
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    • 2012
  • In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

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.

NEW CONDITIONS ON EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Zhengqiu;Zhou, Zheng
    • Journal of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.223-240
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    • 2011
  • In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

GLOBAL EXPONENTIAL STABILITY OF BAM NEURAL NETWORKS WITH IMPULSES AND DISTRIBUTED DELAYS

  • Shao, Yuanfu;Luo, Zhenguo
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.103-117
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    • 2011
  • By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

PERIODIC SOLUTION TO DELAYED HIGH-ORDER COHEN-GROSSBERG NEURAL NETWORKS WITH REACTION-DIFFUSION TERMS

  • Lv, Teng;Yan, Ping
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.295-309
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    • 2010
  • In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

Improved Stability and Stabilization for Sampled-data Control System via Augmented Lyapunov-Krasovskii Functional (합성된 리아프노프 함수법을 통한 샘플링 된 데이터 제어 시스템의 향상된 안정화 조건 및 제어기 설계)

  • Lee, Chang-Ho;Lee, Seung-Hoon;Park, Myeong-Jin;Kwon, Oh-Min
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.1
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    • pp.127-136
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    • 2017
  • This paper investigates improved stability and stabilization criteria for sampled-data control systems. By using a suitable and newly constructed augmented Lyapunov-Krasovskii functional and some recent mathematic techniques such as auxiliary function-based integral inequalities, sufficient conditions for stability and stabilization conditions are derived within the framework of linear matrix inequalities(LMI) form. The superiority and validity of the proposed results are illustrated by three numerical examples.

A New Augmented Lyapunov Functional Approach to Robust Stability Criteria for Uncertain Fuzzy Neural Networks with Time-varying Delays (시변 지연이 존재하는 불확실 퍼지 뉴럴 네트워크의 강인 안정성 판별법에 대한 새로운 리아프노프 함수법)

  • Kwon, Oh-Min;Park, Myeong-Jin;Park, Ju-Hyun;Lee, Sang-Moon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.11
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    • pp.2119-2130
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    • 2011
  • This paper proposes new delay-dependent robust stability criteria for neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's (L-K) functional and use of Finsler's lemma, new stability criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.