Abstract
In this study, sum-of-squares (SOS)-based relaxed stability conditions for the continuous-time Takagi–Sugeno (T–S) fuzzy system are derived using a polynomial non-quadratic Lyapunov function (PNQLF). The proposed methods consist of two approaches. Like the previous studies, the first uses the upper bounds on a time derivative of the fuzzy weighting function (TDFWF), and the other directly uses the TDFWF in order to obtain relaxed results and enlarge the domain of attraction. Moreover, unlike the conventional non-quadratic Lyapunov function, the newly proposed PNQLF uses different fuzzy weighting functions from those of the system in order to solve the existing problems. Finally, the effectiveness of the proposed methods is demonstrated by some numerical examples.
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