Construction of extended Lyapunov functions and control laws for discrete-time TS systems

Non-quadratic Lyapunov functions have now been more and more frequently used for the analysis and design of Takagi-Sugeno fuzzy models. In this paper, we use a delayed non-quadratic Lyapunov function to develop controller design conditions for TS systems. The conditions can easily be formulated as LMIs. We show that in certain cases the developed conditions are more relaxed than current state-of-the-art methods. In order to further reduce the conservativeness, we also extend the conditions to α-sample variation.