Robust guaranteed cost 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:
  • Applied Soft Computing
  • Year:
  • 2011

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Abstract

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz-Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.