Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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H∞ Control for Discrete-Time Fuzzy Markovian Jump Systems with State and Input Time Delays

상태 및 입력 시간지연을 갖는 이산 퍼지 마코비안 점프 시스템의 H∞ 제어

  • 이갑래 (평택대학교 정보통신학과)
  • Received : 2011.09.07
  • Accepted : 2012.02.05
  • Published : 2012.02.25
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Abstract

This paper presents the method for $H_{\infty}$ fuzzy controller design of discrete-time fuzzy Markovian jump systems with state and input time delays. The Takagi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the fuzzy Markovian jump systems with state and input time delays. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller is given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficiency of the proposed design method.

본 논문에서는 상태변수 및 입력변수에 시간지연을 가지는 이산 퍼지 마코비안 점프 시스템의 $H_{\infty}$ 퍼지 제어기 설계 방법을 나타낸다. 시간지연 퍼지 마코비안 점프 시스템은 마코비안 점프 파라미터를 갖는 시간 지연 비선형 시스템을 Takagi-Sugeno 퍼지 모델로 표현된 것이다. 확률 리아프노프(Lyapunov) 함수를 이용하여 폐루프 시스템이 안정하며 $H_{\infty}$ 성능 조건을 만족하는 조건식을 유도한다. 확률 리아프노프 함수는 시스템 모드에 따라 변하는 함수이다. 유도된 조건식으로부터 제어기 존재 조건을 선형행렬부등식으로 나타내며, 제어기는 선형행렬부등식의 해로부터 직접 구할 수 있다. 수치적 예제 및 컴퓨터 시뮬레이션을 통하여 제안된 방법의 타당성을 보인다.

Keywords

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