Robust H∞ control of uncertain fuzzy systems under time-varying sampling

  • Authors:

  • Jun Yoneyama

  • Affiliations:

  • Department of Electrical Engineering and Electronics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

Robust H"~ sampled-data control for uncertain fuzzy systems is discussed. In many practical situations, a system is modeled as a continuous-time fuzzy system, while the control input is the zero-order hold, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the H"~ sampled-data control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, H"~ performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using the Leibniz-Newton formula and free-weighting matrix method for fuzzy time-delay systems under the assumption that sampling time is not greater than some prescribed number. Then, a design method for a robust H"~ sampled-data state feedback controller for uncertain fuzzy systems is proposed. Numerical examples are given to illustrate our robust H"~ sampled-data state feedback control design.