On the conservatism reduction of LMI-based stabilization conditions for Takagi-Sugeno fuzzy systems

Quadratic approach for the stability analysis of multi-models such as Takagi-Sugeno fuzzy systems leads in many cases to conservative results. However, it is shown that nonquadratic approach was an alternative to properly reduce the conservatism and to give more relaxations to the stability and stabilization conditions of fuzzy systems. This paper presents firstly some relaxed stabilization conditions based on common quadratic Lyapunov function (CQLF) and secondly a nonquadratic approach based on fuzzy Lyapunov function (FLF) and focused on the time-derivative of fuzzy membership functions (TDFMF). Sufficient stabilization conditions based on linear matrix inequalities (LMIs) optimization are derived to nonlinear fuzzy controller design. Finally, simulation results are given to demonstrate the effectiveness of the TDFMF-based nonquadratic approach.