Robust stabilization for a class of nonlinear systems: Fuzzy-model-based LMI approach

In this paper, we investigate the robust stabilization problem for a class of nonlinear dynamic systems via fuzzy-model-based state feedback control. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a nonlinear dynamic system. A robust stabilization technique is proposed to override the effect of approximation error in the fuzzy approximation procedure. Next, some sufficient conditions are derived to ensure the robust stabilization of the closed-loop system with fuzzy-type state feedback based controller and guarantee the disturbance attenuation under a desired level. Moreover, these stabilization conditions can be formulated in terms of linear matrix inequalities (LMIs), which can be solved using the convex optimization techniques. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.