Abstract
AbstractThis paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on a new fuzzy Lyapunov function. This new fuzzy Lyapunov function aggregates more information with respect to the membership function variation (time-derivative) via an augmented state vector. This new fuzzy Lyapunov function is not just parametrized by the membership functions variations but it is also based on a polynomial combination of them. To derive LMI based stability condition using the proposed new fuzzy Lyapunov function two ideas are invoked: i) the inclusion of the membership function time-derivative information using a finite number of vectors and, ii) the use of the so-called null term. Two numerical examples are presented to illustrate the improvements.
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