Robust H_∞ Output Feedback Control for T-S Fuzzy Systems: A Non-‎monotonic Approach

This paper proposes robust  output feedback control stabilization for uncertain Takagi–Sugeno (T-S) fuzzy systems via linear matrix inequalities (LMIs). In order to reduce the conservatism associated with T-S fuzzy system, a new form of non-monotonic Lyapunov functions is used. In the non-monotonic approach, the monotonic decrease of the Lyapunov function is relaxed which enables it to increase locally but vanish eventually. Based on the non-monotonic Lyapunov function approach, sufficient conditions for the existence of robust  output feedback control stabilization are derived. The proposed design technique is shown to be less conservative than the existing non-monotonic approach, namely, -samples variations of Lyapunov function. The effectiveness of the proposed approach is further illustrated via numerical example.