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