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박부견,이원일,이석영 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.1
In the field of stability analysis for time-delay systems, finding precise bounds of integral/summationforms of quadratic functions plays a key role in reducing the conservatism. Consequently, there have been manyattempts to develop inequalities yielding much tighter bounds. This paper develops novel inequalities using intermediateterms called auxiliary functions, which includes the existing inequalities as special cases. The stabilityconditions for continuous/discrete time-delay systems are derived in terms of linear matrix inequalities (LMIs) byusing the proposed inequalities with simple numerical examples.
시변 지연 시스템의 안정성 해석을 위한 수치적 기법 연구동향
박부견,이준희,나현우 제어·로봇·시스템학회 2024 제어·로봇·시스템학회 논문지 Vol.30 No.4
Over the past few decades, the stability issues of linear time-varying delay systems have garnered significant attention in academia. Numerous studies have been reported in the literature, focusing on obtaining less conservative stability conditions expressed in the form of Linear Matrix Inequalities. This paper firstly provides an investigation into numerical techniques developed to estimate the upper bound of the single integral term arising from the time derivative of double integral Lyapunov-Krasovskii function (LKF) candidates. Secondly, employing various LKF selection methods and developed numerical techniques, this paper derives six stability criteria of a time-varying delay system. Finally, the effectiveness of various numerical techniques is analyzed and evaluated from the two representative numerical examples.
박부견(PooGyeon Park),이원일(Won Il Lee),이석영(Seok Young Lee) 제어로봇시스템학회 2014 제어·로봇·시스템학회 논문지 Vol.20 No.3
This article surveys the control theoretic study on time delay systems. Since time delay systems are infinite dimensional, there are not analytic but numerical solutions on almost analysis and synthesis problems, which implies that there are a tremendous number of approximated solutions. To show how to find such solutions, several results are summarized in terms of two different axes: 1) theoretic tools like integral inequality associated with the derivative of delay terms, Jensen inequality, lower bound lemma for reciprocal convexity, and Wirtinger-based inequality and 2) various candidates for Laypunov-Krasovskii functionals.
Delay-dependent Robust Stabilization for Systems with Time-varying Delays
고정완,박부견 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.5
This paper extends the results of the stability criterion, introduced in the literature, to the problem of stabilization for systems with time-varying delays. Unfortunately, the delay-dependent stabilization conditions using state/output-feedback controllers are not formulated as LMIs. To achieve a better degree of freedom in relaxing the resultant nonlinear terms, we do not assume any restriction on the form of variables, which is a generally adopted procedure in the structure-imposing relaxation methods. Instead, we develop a congruence transformation that has the effect of gathering the dispersed nonlinear terms and bundling them together into fewer and more intensive non-convex conditions. To relax these, an efficient iterative algorithm is proposed in the form of two-phase-based convex optimization problem. Numerical examples show that the results obtained by these criteria improve the allowable maximal delays over the existing results in the literature.
단단함 이론 기반의 거리 측정 실패 시에 분산 편대제어 기법
권성호,박부견,백주훈,안효성 제어로봇시스템학회 2021 제어로봇시스템학회 국내학술대회 논문집 Vol.2021 No.6
This paper introduces a strategy to be used in the case of failure of measuring distances in distance-based formation control. When a distance-based formation control system fails in sensing distance measurements, an alternative control law is introduced to achieve a target formation shape with only bearing measurements. This statement is discussed from the viewpoint of two rigidity theories, i.e., distance rigidity theory and bearing rigidity theory.