Novel Separation Principle Based $H_\infty$ Observer–Controller Design for a Class of T–S Fuzzy Systems

The observer-based controller design for a T–S fuzzy system subject to external disturbance is investigated in this paper. First, an $H_\infty$ observer is designed to estimate the unknown system states, by a transformation process for system states and the disturbance term, a state feedback $H_\infty$ controller is given. Then, the separation principle for a T–S fuzzy system subject to external disturbance is proposed. With the help of the improved separation principle, the observer and controller can be combined together to make the fuzzy system input-state stable, while the $H_\infty$ index can also be guaranteed. The proposed design approach is applicable for both known and unknown premise variables. In stability analysis, the membership functions derivatives dependent method is proposed to reduce the conservatism. In the simulation part, stability analysis of a three-rule system is carried out to illustrate the conservatism reduction effects in Example 1 ; then, a vessel dynamic positioning control process subject to ocean disturbance is adopted to illustrate the effectiveness of the proposed methods for both known/unknown premise variable cases.