LMI-based design of T-S fuzzy controllers using fuzzy estimator

In this paper we present a systematic design method for PDC (parallel distributed compensation)-type Takagi-Sugeno (T-S) fuzzy control systems which have inaccessible states. Fuzzy state estimator is introduced from existing T-S fuzzy model using the PDC structure of Wang et al. (1995). LMI (linear matrix inequalities) problems which represent the stability of the fuzzy state estimator are derived. Joh et al.'s pole placement constraints idea (1997) for each rules is adopted to determine the estimator gains and they are also revealed as LMI problems. These LMI problems are combined with Joh et al.'s LMI problems for PDC-type T-S fuzzy controller design to yield a systematic design method for PDC-type T-S fuzzy control systems which have inaccessible states. It is proved that the well-known separation property holds. Therefore, feedback control gains and fuzzy state estimator gains can be determined separately. The design method is verified by designing a PDC-type T-S fuzzy controller for an inverted pendulum with a cart.