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 epsiv is developed such that: 1) the
H

_infin
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 epsivmacr for the singular perturbation parameter epsiv, both 1) and 2) are guaranteed for all epsiv isin [0,epsivmacr.] It is shown that the epsiv-dependent controller is well defined for any epsiv isin [0,epsivmacr], and can be reduced to an epsiv-independent one if epsiv is sufficiently small. Finally, a practical example is given to show the feasibility and effectiveness of the obtained method.