H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses

  • Authors:

  • Hongli Dong;Zidong Wang;Huijun Gao

  • Affiliations:

  • Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin and College of Electrical and Information Engineering, Daqing Petroleum Institute, Daqing, China;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, U.K.;Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2009

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Abstract

This paper is concerned with the H∞ fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses. A modified Takagi-Sugeno (T-S) fuzzy model is proposed in which the consequent parts are composed of a set of discrete-time state equations containing a repeated scalar nonlinearity. Such a model can describe some well-known nonlinear systems such as recurrent neural networks. The measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses. Attention is focused on the analysis and design of H∞ fuzzy controllers with the same repeated scalar nonlinearities such that the closed-loop T-S fuzzy control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers, and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities, which can be readily solved by using standard numerical software. Two examples are given to illustrate the effectiveness of the proposed design method.