1 차 시간 지연 시스템에서 고유값 배치에 따른 시스템 파라미터 결정에 관한 연구

다국어 초록 (Multilingual Abstract)

This study proposes an analytical stability region for a first-order time delay system using the Lambert W function and a geometric method. Delay-dependent and -independent stability regions were obtained by defining two functions, such that the characteristic equation is the difference of these functions. The desired rightmost real eigenvalue was assigned. Moreover, the corresponding system parameters were determined. Oscillation or unstable systems can be exponentially stabilized by static state feedback, in which the feedback gain sets are analytically determined using the results of the stability region. The effectiveness of the proposed approach was demonstrated through numerical examples.

목차 (Table of Contents)

• Abstract
• I. 서론
• II. 1차 시간 지연 시스템과 고유값 배치 문제
• III. 수치 예
• IV. 결론
• REFERENCES

참고문헌 (Reference)

1 구배영, "시간 영역 안정도 해석을 통한 외란 관측기 적용시간 지연 시스템의 영점 트래킹 제어" 제어·로봇·시스템학회 24 (24): 406-416, 2018

2 J. Richard, "Time-delay systems : An overview of some recent advances and open problems" 39 (39): 1667-1694, 2003

3 K. Gu, "Survey on recent results in the stability and control of time-delay systems" 125 (125): 158-165, 2003

4 R. Sipahi, "Stability and stabilization of systems with time delay" 31 (31): 38-65, 2011

5 S. A. He, "Stability and performance of first-order linear time-delay feedback systems: an eigenvalue approach" 27 : 2011

6 N. D. Hayes, "Roots of the transcendental equation associated with a certain difference-differential equation" 1 (1): 226-232, 1950

7 H. Shinozaki, "Robust stability analysis of linear time-delay systems by Lambert W function: Some extreme point results" 42 (42): 1791-1799, 2006

8 G. Polya, "Problems and Theorems in Analysis, vol. I: Series, Integral Calculus, Theory of Functions" Springer-Verlag 1972

9 M. K. Grammatikopoulos, "Oscillations of first-order neutral delay differential equations" 120 (120): 510-520, 1986

10 R. M. Corless, "On the Lambert W function" 5 (5): 329-359, 1996

11 O. BREDA, "On characteristic roots and stability charts of delay differential equations" 22 (22): 892-917, 2012

12 S. Amrane, "On Qualitative Properties of Low-Degree Quasipolynomials:Further remarks on the spectral abscissa and rightmost-roots assignment" 61 : 361-381, 2018

13 B. Kim, "Feedback stabilization of first order neutral delay systems using the Lambert W function" 9 (9): 3539-, 2019

14 J. Cermak, "Exact versus discretized stability regions for a linear delay differential equation" 347 : 712-722, 2019

15 C. Chew, "Exact eigenvalue assignment of linear scalar systems with single delay using Lambert W function" 12 (12): 26-33, 2018

16 O. Diekmann, "Delay Equations-Functional, Complex and Nonlinear Analysis vol. 110" Springer Science &Business Media 2012

17 Z. H. Wang, "Calculation of the rightmost characteristic root of retarded time-delay systems via Lambert W function" 318 (318): 757-767, 2008

18 S. Mondie, "Assessing the exact stability region of the singledelay scalar equation via its Lyapunov function" 29 (29): 459-470, 2012

19 I. Jadlovska, "Application of Lambert W function in oscillation theory" 14 (14): 9-17, 2014

20 F. M. Asl, "Analysis of a system of linear delay differential equations" 125 : 215-223, 2003