Robust and optimal fuzzy control: A linear matrix inequality approach

Abstract This paper presents a mixed control design of robust fuzzy control and optimal fuzzy control based on relaxed stability conditions represented by linear matrix inequalities (LMIs). A robust fuzzy controller is designed so as to maximize the norm of the uncertain blocks in a Takagi-Sugeno fuzzy model. Next, an optimal fuzzy controller is designed by solving the minimization problem that minimizes the upper bound of a given quadratic performance index. A mixed control problem that simultaneously considers both of them is defined and is efficiently solved via convex optimization techniques based on LMIs. Finally, a design example for a nonlinear control benchmark problem demonstrates the utility of the mixed control problem based on LMIs.