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Last Updated : 03/2016
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  • A variable step‐size diffusion affine projection algorithm

    JinWoo Yoo, IS Song, JaeWook Shin, PooGyeon Park

    International Journal of Communication Systems

    Abstract This paper presents a new variable step-size diffusion affine projection algorithm (VSS-DAPA) to advance the filter performance of the diffusion affine projection algorithm (DAPA). The proposed VSS strategy is developed for the DAPA, which can solve the distributed estimation problem over diffusion networks well. To obtain the optimal step size reasonably, we seek the update recursion of mean-square deviation (MSD) that is suitable for the DAPA. The step size is optimally given through the minimization for the MSD of the DAPA at each iteration. The derived step size through the MSD minimization improves the filter performance with respect to the convergence and the estimation error in steady state. The results based on simulations demonstrate that the proposed VSS-DAPA performs better than the existing algorithms with a system-identification scenario in diffusion network.
  • New stability analysis for discrete time-delay systems via auxiliary-function-based summation inequalities

    PooGyeon Park, Seok Young Lee, Won Il Lee

    Journal of the Franklin Institute

    AbstractFor the stability analysis of discrete time-delay systems, Jensen inequality has been widely used as the method supporting inequalities for summation quadratic functions. It not only requires a smaller number of decision variables than other approaches but also achieves identical or comparable performance behavior. Based on the analysis for the conservatism of Jensen inequality, however, this paper suggests a new summation inequality say an auxiliary-function-based summation inequality. It is verified that the proposed inequality is a generalized form of the novel summation inequality reported recently. Also, an application to stability analysis for discrete time-delay systems is provided.
  • Improved H∞ state-feedback control for continuous-time Markovian jump fuzzy systems with incomplete knowledge of transition probabilities

    Nam Kyu Kwon, Bum Yong Park, PooGyeon Park, In Seok Park

    Journal of the Franklin Institute

    AbstractThis paper proposes the improved H∞ state-feedback control for Markovian jump fuzzy systems (MJFSs) with incomplete knowledge of transition probabilities. From the fundamental first-order properties of the transition rates, two second-order properties are introduced without information on the lower and upper bounds of the transition rates, differently from other approaches in the literature. Based on these properties, this paper uses all possible slack variables into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.
  • A combined first-and second-order reciprocal convexity approach for stability analysis of systems with interval time-varying delays

    Won Il Lee, Seok Young Lee, PooGyeon Park

    Journal of the Franklin Institute

    AbstractFor the interval time-varying delay systems, Jensen inequality lemma yields some terms with the inverse of convex and squared convex parameters, which often makes it difficult to find their bounds. Recently, reciprocal and second-order reciprocal convexity approaches have been proposed to handle the difficulties with a set of convex parameters and a set of squared convex parameters, respectively, but these approaches do not investigate the relation between the two sets. This paper offers much tighter bounds of those terms utilizing the relations among the two sets with the lower bound lemma. Based on the new approach and Lyapunov theory, less conservative stability criteria for time delay systems are developed. To show the effectiveness of the new approach, two numerical examples are given.
  • Auxiliary function-based integral/summation inequalities: Application to continuous/discrete time-delay systems

    PooGyeon Park, Won Il Lee, Seok Young Lee

    International Journal of Control, Automation and Systems

    AbstractIn the field of stability analysis for time-delay systems, finding precise bounds of integral/summation forms of quadratic functions plays a key role in reducing the conservatism. Consequently, there have been many attempts to develop inequalities yielding much tighter bounds. This paper develops novel inequalities using intermediate terms called auxiliary functions, which includes the existing inequalities as special cases. The stability conditions for continuous/discrete time-delay systems are derived in terms of linear matrix inequalities (LMIs) by using the proposed inequalities with simple numerical examples.
  • Special issue on time-delay systems and their applications

    Ju H Park, PooGyeon Park

    International Journal of Control, Automation and Systems

    Abstract
  • Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation

    Nam Kyu Kwon, Bum Yong Park, PooGyeon Park

    Optimal Control Applications and Methods

    Abstract This paper proposes less conservative stabilization conditions for Markovian jump systems with incompleteknowledge of transition probabilities and input saturation. The transition rates associated with the transitionprobabilities are expressed in terms of three properties, which do not require the lower and upper bounds ofthe transition rates, differently from other approaches in the literature. The resulting conditions are convertedinto the second-order matrix polynomial of the unknown transition rates. The polynomial can be representedas quadratic form of vectorized identity matrices scaled by one and the unknown transition rates. And then,the LMI conditions are obtained from the quadratic form. Also, an optimization problem is formulated to?nd the largest estimate of the domain of attraction in mean square sense of the closed-loop systems. Finally,two numerical examples are provided to illustrate the effectiveness of the derived stabilization conditions.Copyright ⓒ 2016 John Wiley & Sons, Ltd.
  • A diffusion subband adaptive filtering algorithm for distributed estimation using variable step size and new combination method based on the MSD

    Ji-Hye Seo, Sang Mok Jung, PooGyeon Park

    Digital Signal Processing

    Abstract This paper proposes a novel diffusion subband adaptive filtering algorithm for distributed networks. To achieve a fast convergence rate and small steady-state errors, a variable step size and a new combination method is developed. For the adaptation step, the upper bound of the mean-square deviation (MSD) of the algorithm is derived and the step size is adaptive by minimizing it in order to attain the fastest convergence rate on every iteration. Furthermore, for a combination step realized by a convex combination of the neighbor-node estimates, the proposed algorithm uses the MSD, which contains information on the reliability of the estimates, to determine combination coefficients. Simulation results show that the proposed algorithm outperforms the existing algorithms in terms of the convergence rate and the steady-state errors.