For the output feedback control problem of a T-S fuzzy system with unknown premise variables and external disturbances, a new observer-based controller H1 robust synthesis approach is proposed. To utilize the membership functions more effectively, a membership functions constructed vector is used as new premise variables. Then the error items which are induced by unknown premise variables are decoupled into a new T-S fuzzy system. For the derived stability and robustness conditions in complex bilinear matrix inequality form, more relaxed sufficient conditions which can be solved directly by convex optimization method are proposed. Finally, a suspended floater control system based simulation process is carried out. The conservatism reduction effects among traditional and decoupling approaches are given, the state estimation effects of the observer and control performances are also verified.

For the stability analysis of a polynomial fuzzy system, a new polynomial membership function approach is proposed to reduce conservatism. In this article, based on a state-feedback closed-loop system, a polynomials fitting method is utilized, and an improved membership function transformation technique is proposed to approximate the membership functions of the fuzzy system. Then, the membership-function-dependent polynomial-based stability conditions are derived. The obtained polynomial membership functions and approximation errors will be involved in the stability analysis process. Based on the sum-of-squares optimization technique, polynomial conditions can be directly solved. Finally, by several numerical and practical examples, conservatism reduction effects are shown by comparisons with existing methods.

The observer-based controller design for a T-S fuzzy system subject to external disturbance is investigated in this paper. First, an H$\infin$ observer is designed to estimate the unknown system states, by a transformation process for system states and the disturbance term, a state feedback H$\infin$ 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$\infin$ 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.

In this paper, finite-time attitude coordinated control for spacecraft formation flying (SFF) subjected to input saturation is investigated. More specifically, a bounded finite-time state feedback control law is first developed with the assumption that both attitude and angular velocity signals can be measured and transmitted between formation members. Then, a bounded finite-time output feedback controller is designed with the addition of a filter, which removes the requirement of the angular velocity measurements. In both cases, actuator saturation is explicitly taken into account, and the homogeneous system method is employed to demonstrate the finite-time stability of the closed-loop system. Numerical simulation results are presented to illustrate the efficiency of the proposed control schemes.