Multiobjective Control for T-S Fuzzy Singularly Perturbed Systems

This paper investigates the problem of multiobjective control for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed systems. Based on a linear matrix inequality (LMI) approach, a state feedback controller that depends on the singular perturbation parameter epsilon is developed such that: 1) the H(infinity) performance of the resulting closed-loop system is less than or equal to some prescribed value; 2) the closed-loop poles of each local system are within a prespecified LMI stability region; and 3) for a given upper bound (epsilon) over bar for the singular perturbation parameter epsilon, both 1) and 2) are guaranteed for all epsilon is an element of (0, (epsilon) over bar). It is shown that the epsilon-dependent controller is well defined for any epsilon is an element of (0, (epsilon) over bar), and can be reduced to an epsilon-independent one if epsilon is sufficiently small. Finally, a practical example is given to show the feasibility and effectiveness of the obtained method.