한국항행학회논문지 (Journal of Advanced Navigation Technology)

  • 제20권5호
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  • Pages.475-481
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  • 2016
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  • 1226-9026(pISSN)
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  • 2288-842X(eISSN)
한국항행학회 (The Korean Navigation Institute)
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시변 지연시간을 갖는 이산 구간 시변 시스템의 안정조건

Stability Condition for Discrete Interval Time-varying System with Time-varying Delay Time

  • 한형석 (가천대학교 전자공학과)
  • Han, Hyung-seok (Department of Electronic Engineering, Gachon University)
  • 투고 : 2016.09.30
  • 심사 : 2016.10.12
  • 발행 : 2016.10.30
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초록

본 논문에서는 상태변수에 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 안정조건을 새롭게 제안한다. 고려한 시스템은 지연 없는 상태변수에 대한 시스템 행렬과 지연 상태변수에 대한 시스템 행렬이 시변 구간 행렬로 표현되며, 지연시간도 구간에 대하여 시변인 특성을 갖는다. 제안된 안정조건은 리아프노프 안정 이론을 이용하여 유도되며, 매우 간단한 부등식의 형태로 표현된다. 본 논문에서는 기존의 시불변 구간 행렬의 안정성 문제를 시변 구간 행렬의 안정성 문제로 확장하고, 기존에 발표된 결과를 포함하는 강력한 안정조건이 유도된다. 이 안정조건의 유도과정에서는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 구하지 않아도 된다. 또한, 기존의 결과들과의 비교를 통하여 제안된 안정조건이 많은 기존 안정 조건들을 포함할 수 있음을 보인다. 기존 수치예제를 일반적인 형태로 확장하였고 이에 대하여 새로운 안정조건의 확장성과 효용성을 확인한다.

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

키워드

참고문헌

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피인용 문헌

  1. 시변 지연시간을 갖는 이산 구간 시변 시스템의 시변 불확실성의 안정범위 vol.21, pp.6, 2016, https://doi.org/10.12673/jant.2017.21.6.608
  2. 비구조화된 불확실성과 시변 지연을 갖는 이산 시스템의 안정 조건 vol.22, pp.6, 2016, https://doi.org/10.12673/jant.2018.22.6.630
  3. 비구조화 불확실성을 갖는 양의 시변 이산 구간 시스템의 안정 조건 vol.23, pp.6, 2016, https://doi.org/10.12673/jant.2019.23.6.577
  4. 비구조화된 불확실성을 갖는 이산 지연 시스템의 새로운 안정조건 vol.24, pp.6, 2020, https://doi.org/10.12673/jant.2020.24.6.607