Fuzzy control system design and stability analysis for ship lift feedback fin stabilizer

A more precise T-S fuzzy model was established to approximate the nonlinear model of ship rolling movement. Based on fuzzy partition of the input space, two new sufficient conditions under which the closed-loop T-S fuzzy control system is asymptotically stable in the large were obtained by constructing piecewise smooth Lyapunov function. The new sufficient conditions, which only required finding a common positive definite matrix and a positive semi-definite matrix in each subspace, reduced the conservatism and difficulty of the former stability conditions since the structural information of the premises and the interactions among the local subsystems were utilized sufficiently. The comparison of the relationships among the stability conditions we proposed was concluded in a rigorous manner. Utilizing parallel distributed compensation (PDC) principle and linear system theory, a systematic design method of T-S fuzzy controller was investigated and a resulting T-S fuzzy controller of ship lift feedback fin was applied to the original nonlinear model of ship rolling movement. The computer simulation demonstrates the validity and superiority of the proposed systematic design method and the stability conditions.