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# Journal of Professor & SPaC member

Last Updated : 03/2016
• ## Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

Seok Young Lee, Won Il Lee, PooGyeon Park

Journal of the Franklin Institute

Abstract Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays.
• ## Delays-Dependent region partitioning approach for stability criterion of linear systems with multiple time-varying delays

Kab Seok Ko, Won Il Lee, PooGyeon Park, Dan Keun Sung

Automatica

Abstract This paper considers a delay-dependent stability criterion for linear systems with multiple time-varying delays. To exploit all possible information for the relationships among the marginally delayed states (x(t−τiM)x(t−τi+1M)), the exactly delayed states (x(t−τi(t)),x(t−τi+1(t))), and the current state x(t) for each pair (i,i+1) of time-varying delays, a delays-dependent region partitioning approach in double integral terms is proposed. By applying the Wirtinger-based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning, a stability criterion is derived in terms of linear matrix inequalities. Numerical examples show that the resulting criterion outperforms the existing one in literature.
• ## \mathcal {H} _\infty  H∞ state-feedback control for continuous-time Markovian jump fuzzy systems using a fuzzy weighting-dependent Lyapunov function

Nam Kyu Kwon, In Seok Park, PooGyeon Park

Nonlinear Dynamics

Abstract This paper proposes a method for designing an HH∞ state-feedback fuzzy controller for continuous-time Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates. To find HH∞ control for level γγ, the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) for the MJFSs based on a fuzzy weighting-dependent Lyapunov function. Besides, to derive less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Finally, three examples are provided to verify the effectiveness of the proposed method.
• ## Stabilization condition of one-step receding horizon control for discrete-time linear systems with model uncertainties

Nam Kyu Kwon, In Seok Park, PooGyeon Park, Chaneun Park

IEEE Transactions on Automatic Control

Abstract For the dynamic output-feedback stabilization of continuous-time singular Markovian jump systems, this paper introduces the necessary and sufficient condition, whereas the previous research works suggested the sufficient conditions. A special choice of the block entries of Lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities. A numerical example shows the validity of the derived results.
• ## Dynamic output-feedback stabilisation for Markovian jump systems with incomplete transition description and input quantisation: linear matrix inequality approach

Nam Kyu Kwon, Chan-eun Park, PooGyeon Park

IET Control Theory & Applications

Abstract In this study, a dynamic output-feedback stabilisation problem for Markovian jump systems (MJSs) with incomplete transition description and input quantisation is investigated. While the previous researches about output-feedback stabilisation for MJSs assumed that the transition rates are completely known, a more general situation where the transition rates are partly unknown is considered. Moreover, the proposed controller includes non-linear control part to eliminate the effect of input quantisation. Two numerical examples are provided to demonstrate the feasibility of the proposed dynamic output-feedback controller.
• ## Steady-state mean-square deviation analysis of the sign subband adaptive filter

J Shin, J Yoo, P Park

Electronics Letters

Abstract  The steady-state mean-square deviation (MSD) analysis of the sign subband adaptive filter is proposed. The proposed analysis is derived by the update recursion of the MSD using Price’s theorem and chi-distribution in stationary environments. Experimental results show that the proposed analysis is very close to simulated results not only for white input but also for coloured input signals.
• ## Stabilization of a bias-compensated normalized least-mean-square algorithm for noisy inputs

Sang Mok Jung, PooGyeon Park

IEEE Transactions on Signal Processing

Abstract  This paper proposes a stability-guaranteed bias-compensated normalized least-mean-square (BC-NLMS) algorithm for noisy inputs. The bias-compensated algorithms require the estimated input noise variance in the elimination process of the bias caused by noisy inputs. However, the conventional methods of estimating the input noise variance in those algorithms might cause the instability for a specific situation. This paper first analyzes the stability of the BC-NLMS algorithm by investigating the dynamics of both the mean deviation and the mean-square deviation in the BC-NLMS algorithm. Based on the analysis, the estimation of the input noise variance and the adjustment of the step size are carried out to perform a stabilization as well as a performance enhancement in terms of a steady-state error and a convergence rate. Simulations in system identification and acoustic echo cancellation scenarios with noisy inputs show that the proposed algorithm outperforms the existing bias-compensated algorithms in the aspect of the stability, the steady-state error, and the convergence rate.
• ## Improved H∞ Control for Discrete-Time Markovian Jump Systems with Partly Unknown Transition Probabilities and Saturated Actuator

In Seok Park, Nam Kyu Kwon, PooGyeon Park

정보 및 제어 논문집

Abstract This paper considers the problem of H∞ control for Markovian jump systems with partly unknown transition probabilities and input saturation. Using the convex property of normalized mode transition probabilities, less conservative H∞ stochastic stabilization conditions for discrete-time Markovian jump systems with partly unknown transition probabilities and input saturation are derived. Then, the derived conditions are represented as linear matrix inequalities (LMIs) conditions. The numerical examples will show that the proposed theorem exhibited better performance in view of the minimum cost
• ## 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.
• ## H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities

Nam Kyu Kwon, In Seok Park, PooGyeon Park

Applied Mathematics and Computation

AbstractThis paper proposes a H∞ state-feedback control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given, a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered. Moreover, in contrast to the singular Markovian jump systems studied recently, the proposed method does not require any tuning parameters that arise when handling non-convex terms related to the mode-dependent Lyapunov matrices and the corresponding self-mode transition rates. Also, this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to demonstrate the performance of H∞ mode-dependent control.