Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
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Fuzzy H∞ Filtering for Discrete-Time Nonlinear Markovian Jump Systems with State and Output Time Delays

상태 및 출력 시간지연을 갖는 이산 비선형 마코비안 점프 시스템의 퍼지H∞ 필터링

  • Lee, Kap Rai (Dept. of Information & Communication, Pyeongtaek University)
  • 이갑래 (평택대학교 정보통신학과)
  • Received : 2013.03.01
  • Accepted : 2013.05.25
  • Published : 2013.06.28
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Abstract

This paper deals with fuzzy $H_{\infty}$ filtering problem of discrete-time nonlinear Markovian jump systems with state and output time delays. The purpose is to design fuzzy $H_{\infty}$ filter such that the corresponding estimation error system with time delays and initial state uncertainties is stochastically stable and satisfies an $H_{\infty}$ performance level. A sufficient condition for the existence of fuzzy $H_{\infty}$ filter is given in terms of matrix inequalities. In order to relax conservatism, a stochastic mode dependent fuzzy Lyapunov function is employed. The Lyapunov function not only is dependent on the operation modes of system, but also includes the fuzzy membership functions. An illustrative example is finally given to show the applicability and effectiveness of the proposed method.

본 논문에서는 상태 및 출력변수에 시간지연을 가지는 이산 비선형 마코비안 점프시스템의 퍼지 $H_{\infty}$ 필터 설계 방법을 다룬다. 리아프노프(Lyapunov) 함수를 이용하여 상태추정 오차시스템이 확률적 안정하며 외부외란 및 초기값 불확실성에 대하여 $H_{\infty}$ 성능을 만족하는 조건식을 유도하고 필터 존재 조건을 선형행렬부등식으로 나타낸다. 완화된 필터 존재 조건식을 유도하기 위하여 리아프노프 함수 선택 시에 시스템 모드에 종속적일뿐만 아니라 퍼지 멤버십 함수를 포함하는 확률-퍼지 리아프노프 함수를 선택한다. 또한 $H_{\infty}$ 성능 조건식 유도 시에 외부외란 뿐만 아니라 최기값 불확실성을 고려한다. 수치적 예제 및 컴퓨터 시뮬레이션을 통하여 제안된 방법의 타당성을 보인다.

Keywords

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