Control of nonlinear systems by fuzzy observer-controller with unmeasurable premise variables

In this paper, we investigate the stability of Takagi-Sugeno (T-S) fuzzy-model-based (FMB) observer-control system. Premise membership functions depending on unmeasurable premise variables are considered to enhance the flexibility and applicability of the fuzzy observer-controller. The fuzzy observer is designed to estimate the system states and the estimated states are employed for state-feedback control of nonlinear systems. Convex stability conditions are obtained through matrix decoupling technique so that a solution can be searched using convex programming techniques. The proposed analysis is able to reduce the number of predefined scalars by adequately choosing the augmented vector. Nonetheless, due to the mismatched premise membership functions between the fuzzy model and fuzzy observer-controller, it complicates the stability analysis which potentially leads to conservative stability conditions. To alleviate the problem, the stability conditions are relaxed by membership-function-dependent approach which takes the information of membership functions into consideration in the stability analysis. Simulation examples are provided to demonstrate the feasibility and relaxation of proposed FMB observer-control scheme.