Brief Paper - Relaxed stabilisation criterion for discreteT-S fuzzy systems by minimum-type piecewise non-quadratic Lyapunov function

Piecewise Lyapunov functions and non-quadratic Lyapunov functions have been employed to analyse Takagi-Sugeno (T-S) fuzzy systems for getting relaxed results in the literature. Nevertheless, until now piecewise non-quadratic Lyapunov functions have not been used to design T-S fuzzy control systems. Motivated by the aforementioned concerns, this study utilises the minimum-type piecewise non-quadratic Lyapunov function to design the discrete T-S fuzzy control system. Based on the piecewise non-quadratic Lyapunov function, the switching non-parallel distributed compensation control law is proposed to obtain the relaxed stabilisation criterion. Owing to that some conditions of the proposed criterion are bilinear matrix inequalitiy conditions, the particle swarm optimisation algorithm is applied for finding out the solution of the criterion. An example is provided to illustrate the effectiveness of the proposed criterion.