Robust H nonlinear modeling and control via uncertain fuzzy systems

Ji Chang Lo, Min Long Lin

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Abstract

In theory, an Algebraic Riccati Equation (ARE) scheme applicable to robust H quadratic stabilization problems of a class of uncertain fuzzy systems representing a nonlinear control system is investigated. It is proved that existence of a set of solvable AREs suffices to guarantee the quadratic stabilization of an uncertain fuzzy system while satisfying H -norm bound constraint. It is also shown that a stabilizing control law is reminiscent of an optimal control law found in linear quadratic regulator, and a linear control law can be immediately discerned from the stabilizing one. In practice, the minimal solution to a set of parameter dependent AREs is somewhat stringent and, instead, a linear matrix inequalities formulation is suggested to search for a feasible solution to the associated AREs. The proposed method is compared with the existing fuzzy literature from various aspects.

Original languageEnglish
Pages (from-to)189-209
Number of pages21
JournalFuzzy Sets and Systems
Volume143
Issue number2
DOIs
StatePublished - 16 Apr 2004

Keywords

  • Algebraic Riccati equation
  • Linear matrix inequalities (LMI)
  • Norm-bounded uncertainty
  • Quadratic stabilization
  • Takagi-Sugeno fuzzy model

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