A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi–Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.