Stabilization conditions of Takagi-Sugeno fuzzy systems based on the fuzzy Lyapunov functions under the imperfect premise matching

This paper presents a novel stabilization conditions with imperfect premise matching method for nonlinear systems that are represented by the Takagi-Sugeno (T-S) fuzzy model. The term imperfect premise matching has the advantage that the fuzzy controller can be modelled simply by discordance between premise rules of the T-S fuzzy model and those of fuzzy controller. For this reason, the fuzzy controller guaranteed the design flexibility result in decreasing the structural complexity of the fuzzy system. Also, the modified fuzzy Lyapunov function is employed for reducing the conservativeness in controller design and easing the restriction of the conventional fuzzy Lyapunov function. The sufficient conditions for the stabilization of the T-S fuzzy system are derived in terms of the linear matrix inequalities (LMIs). The numerical example is simulated to show the feasibility and effectiveness of the proposed method.