JOURNALS

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Last Updated : 03/2019
  • Stability analysis for systems with time-varying delay via orthogonal-polynomial-based integral inequality

    JunMin Park, PooGyeon Park

    IFAC-PapersOnLine

    Abstract This paper proposes an integral inequality related to the state vector for systems with time-varying delay and exploits component vectors of the proposed inequality for constructing a Lyapunov-Krasovskii functional. The proposed inequality is based on orthogonal-polynomial-based integral inequality. The component vectors of the proposed inequality have the relation in terms of time-varying delay with those of the orthogonal-polynomial-based integral inequality. Also, the time-derivative of the component vectors of the proposed inequality are represented by those of the orthogonal-polynomial-based integral inequality. The Lyapunov-Krasovskii functional is constructed by utilizing the component vectors of the proposed inequality and the orthogonal-polynomial-based integral inequality. Based on the the Lyapunov-Krasovskii functional, a stability criterion is derived in terms of linear matrix inequalities. Simulation results show that the proposed criterion is less conservative than the criteria in the literature.
  • Dynamic output‐feedback control for continuous‐time singular Markovian jump systems

    Chan‐eun Park, Nam Kyu Kwon, PooGyeon Park

    International Journal of Robust and Nonlinear Control

    Abstract This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control.
  • Adaptive regularisation for normalised subband adaptive filter: mean-square performance analysis approach

    JaeWook Shin, JinWoo Yoo, PooGyeon Park

    IET Signal Processing

    Abstract The normalised subband adaptive filter (NSAF) is a useful adaptive filter, which improves the convergence rate compared with the normalised least mean-square algorithm. Most analytical results of the NSAF set the regularisation parameter set to zero or present only steady-state mean-square error performance of the regularised NSAF (ε-NSAF). This study presents a mean-square performance analysis of ε-NSAF, which analyses not only convergence behaviour but also steady-state behaviour. Furthermore, a novel adaptive regularisation for NSAF (AR-NSAF) is also developed based on the proposed analysis approach. The proposed AR-NSAF selects the optimal regularisation parameter that leads to improving the performance of the adaptive filter. Simulation results comparing the proposed analytical results with the results achieved from the simulation are presented. In addition, these results verify that the proposed AR-NSAF outperforms the previous algorithms in a system-identification and acoustic echo-cancellation scenarios.
  • A Less Conservative Stability Criterion for Discrete-Time Lur’e Systems With Sector and Slope Restrictions

    Junmin Park, Seok Young Lee, PooGyeon Park

    IEEE Transactions on Automatic Control

    Abstract This paper proposes a less conservative stability criterion for discrete-time Lur’e systems with sector and slope restrictions by constructing a novel Lyapunov functional. Compared with the Lyapunov functional in the literature, this paper fully utilizes the sector and slope restrictions to the novel Lyapunov functional which includes integral terms involved with the sector restriction of the nonlinearities ϕ(yi) and ϕ(yi+1) , integral terms involved with the slope restriction between ϕ(yi) and ϕ(yi+1) , and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms. The positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms. Based on the novel Lyapunov functional, an improved stability criterion is derived in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion.
  • Bessel summation inequalities for stability analysis of discrete‐time systems with time‐varying delays

    Seok Young Lee, JunMin Park, PooGyeon Park

    International Journal of Robust and Nonlinear Control

    Abstract This paper is concerned with the stability analysis problems of discrete‐time systems with time‐varying delays using summation inequalities. In the literature focusing on the Lyapunov‐Krasovskii approach, the Jensen integral/summation inequalities have played important roles to develop less conservative stability criteria and thus have been widely studied. Recently, the Jensen integral inequality was successfully generalized to the Bessel‐Legendre inequalities constructed with arbitrary‐order Legendre polynomials. It was also shown that general inequality contributes to the less conservatism of stability criteria. In the case of discrete‐time systems, however, the Jensen summation inequality are hardly extensible to general ones since there have still not been general discrete orthogonal polynomials applicable to the developments of summation inequalities. Motivated by such observations, this paper proposes novel discrete orthogonal polynomials and then successfully derives general summation inequalities. The resulting summation inequalities are discrete‐time counterparts of the Bessel‐Legendre inequalities but are not based on the discrete Legendre polynomials. By developing hierarchical stability criteria based on the proposed summation inequalities, the effectiveness of the proposed approaches is demonstrated via three numerical examples for the stability analysis of discrete‐time systems with time‐varying delays.
  • Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates

    In Seok Park, Nam Kyu Kwon, PooGyeon Park

    Nonlinear Dynamics

    Abstract This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with partly unknown transition rates. First of all, for the augmented systems, the stabilization conditions are formulated in terms of non-convex matrix inequalities. For these conditions, this paper successfully derives new necessary and sufficient conditions in the form of linear matrix inequalities under partly unknown transition rates by using the variable elimination technique. Two numerical examples are provided to demonstrate the validity of the derived results.
  • H∞ sampled-state feedback control for synchronization of chaotic Lur’e systems with time delays

    JunMin Park, PooGyeon Park

    Journal of the Franklin Institute

    Abstract This paper investigates H∞ sampled-state feedback control for synchronization of chaotic Lur’e systems with time delays under the aperiodic samplings. First, this paper proposes an improved stability criterion for sampled-state feedback control to synchronize the chaotic Lur’e systems with time delays under aperiodic samplings by constructing a novel Lyapunov–Krasovskii functional. Compared with the literature, the novel Lyapunov–Krasovskii functional utilizes the fragmented state and its state-space model which is defined between the last sampling instant and the present time. Second, this paper introduces an H∞ performance index for H∞ sampled-state feedback control of synchronization error systems considering the state-space model of the fragmented state. Based on the proposed Lyapunov–Krasovskii functional and the H∞ performance index, the stability criterion and the H∞ control criterion are derived in terms of linear matrix inequalities, respectively. A numerical example shows the effectiveness of the proposed criterion.
  • Optimal H∞ filtering for singular Markovian jump systems

    Chan-eun Park, Nam Kyu Kwon, PooGyeon Park

    Systems & Control Letters

    Abstract This paper considers H∞ H∞ filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H∞ H∞ filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H∞ H∞ filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H∞ H∞ filtering.
  • An improved fragmentation approach to sampled-data synchronization of chaotic Lur’e systems

    JunMin Park, Seok Young Lee, PooGyeon Park

    Nonlinear Analysis: Hybrid Systems

    Abstract This paper considers the sampled-data synchronization problem for two identical chaotic Lur’e systems. Under aperiodic samplings, the output of the chaotic Lur’e systems is available only at sampling instants. An improved fragmentation approach addresses a system description of the fragmented state located between the last sampling instant and present time. The sampled output of the fragmented state system is updated only at sampling instants, like the identical chaotic Lur’e systems. Thus, utilizing the additional information on the fragmented state system helps in handling the sampling interval. In the looped-functional framework, a sampled-data synchronization criterion is proposed for stability analysis and control synthesis about stabilization in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.
  • A linear programming approach for stabilization of positive Markovian jump systems with a saturated single input

    In Seok Park, Nam Kyu Kwon, PooGyeon Park

    Nonlinear Analysis: Hybrid Systems

    Abstract This paper proposes a linear programming approach for stabilization of positive Markovian jump systems (PMJSs) with a saturated single input. The proposed approach first derives a sufficient condition for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. By introducing an intermediate scalar whose absolute value is less than the absolute value of product of nonnegative vector of the linear co-positive Lyapunov function and input matrix and constructing a special form of the controller gains, this approach obtains a modified condition applicable for the linear programming. Finally, four numerical examples show that the proposed approach gives the larger domain of attraction than the existing approach based on the quadratic Lyapunov function.