Relaxed stability condition for polynomial fuzzy system: Non-quadratic Lyapunov function approach

In this paper, relaxed stability of polynomial fuzzy system is considered. Proposed relaxed stability condition is based on the non-quadratic Lyapunov function (NQLF). Since the condition that contains the time derivative of the fuzzy weighting function (FWF) cannot be casted into linear matrix inequality (LMI) condition, various researches arbitrarily set the bound of its magnitude. To solve this problem, in this paper, the stability condition is directly calculated without setting the bound of magnitude of the time derivative of the FWF, and the condition is casted into sum-of-square (SOS) condition. Finally, to prove the superiority of proposed method, simulation example is given.