New approaches to observer design and stability analysis for T-S fuzzy system with multiplicative noise

The problem of observer design and stability analysis for T-S fuzzy system with multiplicative noise is investigated in this paper. Based on the fuzzy Lyapunov function, a membership function based global stable non-parallel distributed compensation observer is developed for the T-S fuzzy system. Then we give an improved membership function dependent stability analysis approach, which involves the calculated values of the membership function and its derivatives. The conservativeness of stability conditions for the observer is much relaxed than the existing methods, and these conditions can be formulated as LMIs (linear matrix inequalities), which can be effectively solved by convex optimization techniques. An example is provided to illustrate the effectiveness of proposed method.