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Last Updated : 03/2016
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  • Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functionals

    Won Il Lee, Seok Young Lee, PooGyeon Park

    Neurocomputing

    Abstract This paper considers the stability problem of recurrent neural networks with interval time-varying delays. Based on a new augmented Lyapunov-Krasovskii functional that contains four triple integral terms and additional terms obtained from the activation function condition, a stability condition is derived in terms of linear matrix inequalities (LMIs). Also, a further improved stability criterion is derived by bounding the derivative of a special case of the proposed Lyapunov?Krasovskii functional based on a new inequality proposed in Seuret and Gouaisbaut (2013) [27]. A numerical example shows the improvement of the proposed approach both in terms of computational complexity and conservatism.
  • Auxiliary Function-based Integral Inequalities for Quadratic Functions and their Applications to Time-delay Systems

    PooGyeon Park, Won Il Lee, Seok Young Lee

    Journal of The Franklin Institute

    Abstract Finding integral inequalities for quadratic functions plays a key role in the field of stability analysis. In such circumstances, the Jensen inequality has become a powerful mathematical tool for stability analysis of time-delay systems. This paper suggests a new class of integral inequalities for quadratic functions via intermediate terms called auxiliary functions, which produce more tighter bounds than what the Jensen inequality produces. To show the strength of the new inequalities, their applications to stability analysis for time-delay systems are given with numerical examples.

  • {\ mathcal {H}} _\ infty control of continuous-time uncertain linear systems with quantized-input saturation and external disturbances

    Bum Yong Park, Sung Wook Yun, PooGyeon Park

    Nonlinear Dynamics

    Abstract Abstract This paper introduces an { mathcal {H}} _ infty state- feedback controller for uncertain linear systems with quantized-input saturation and external disturbances. The proposed controller comprises two parts: a linear control part to achieve an H∞ performance against model uncertainties and the mismatched part of the disturbances and a nonlinear control part to eliminate the effect of input quantization and the matched part of the disturbances, which provides the better disturbance attenuation performance than a controller that deals with a unified disturbance regardless of the presence of matched and mismatched parts. Simulation results confirm the effectiveness of the proposed controller.

  • An Improved NLMS Algorithm in Sparse Systems Against Noisy Input Signals

    Jin Woo Yoo, Jae Wook Shin, PooGyeon Park

    Electronics Letters

    Abstract This brief proposes a novel normalized least mean square algorithm that is characterized by robustness against noisy input signals. To compensate for the bias caused by the input noise that is added at the filter input, a derivation method based on reasonable assumptions finds a bias-compensating vector. Moreover, the proposed algorithm has a fast convergence rate when applied to sparse systems, owing to its L0-norm cost in the proposed update equation. The simulation results verify that the proposed algorithm improves the performance of the filter, in terms of system identification in sparse systems, in the presence of noisy input signals.
  • Efficient variable step-size diffusion normalised least-mean-square algorithm

    Sang Mok Jung, Ji-Hye Seo, PooGyeon Park

    Electronics Letters

    Abstract An efficient variable step-size diffusion normalised least-mean-square algorithm is proposed via a mean-square deviation (MSD) analysis for the distributed estimation. The proposed algorithm has two distinguishing features for computational efficiency. In the adaptation step, an intermittent adaptation rule that dynamically adjusts an update interval is proposed to reduce the redundant updates. In the diffusion step, instead of the existing combination rules, a selection rule is proposed to select the intermediate estimate of the most reliable node among its neighbour nodes for the estimate at each node. Moreover, to achieve both fast convergence rate and low steady-state error, a variable step size is obtained by minimising the MSD.
  • An improved stability criterion for discrete-time Lur’e systems with sector-and slope-restrictions

    Bum Young Park, PooGyeon Park, Nam Kyu Kwon

    Automatica

    Abstract This paper introduces an improved stability criterion for discrete-time Lur’e systems with sector- and slope-restrictions. For the stability criterion, a Lur’e Lyapunov functional candidate is constructed to include quadratic terms and integration terms with nonlinearities. To handle the resulting integration terms in the Lyapunov difference, there is proposed a new bound lemma where the integration terms are relaxed into the second-order terms by the geometric point of view. In addition, an appropriate weighting method uses slack variables from the sector- and slope-restrictions. In the overall derivation, the stabilization condition is formulated in terms of a parameterized linear matrix inequality (PLMI), which is then converted into the linear matrix inequality. An example illustrates that the proposed criterion presents a less conservative result than the previous criteria in the literature.

  • A variable step-size diffusion normalized least-mean-square algorithm with a combination method based on mean-square deviation

    Sang Mok Jung, Ji-Hye Seo, PooGyeon Park

    Circuits, Systems, and Signal Processing

    Abstract A novel diffusion normalized least-mean-square algorithm is proposed for distributed network. For the adaptation step, the upper bound of the mean-square deviation (MSD) is derived instead of the exact MSD value, and then, the variable step size is obtained by minimizing it to achieve fast convergence rate and small steady-state error. For the diffusion step, the individual estimate at each node is constructed via the weighted sum of the intermediate estimates at its neighbor nodes, where the weights are designed by using a proposed combination method based on the MSD at each node. The proposed MSD-based combination method provides effective weights by using the MSD at each node as a reliability indicator. Simulations in a system identification context show that the proposed algorithm outperforms other algorithms in the literatures.