Positivstellensatz relaxation for sum-of-squares stabilization conditions of polynomial fuzzy systems

This paper presents a stability analysis of polynomial fuzzy systems by applying a piecewise-polynomial-Lyapunov function approach. Polynomial fuzzy system is a general form of the well-known T-S fuzzy system. The stabilization conditions of polynomial fuzzy system are derived based on the Lyapunov stability theory that are represented in terms of sum-of-squares (SOS) and solved by utilizing the SOSOPT that is a free-third party MATLAB toolbox. A Positivstellensatz relaxation for SOS stabilization conditions of polynomial fuzzy systems is also performed in this paper to get a more relaxed result compared with other existing results. A benchmark design example is presented to show the effectiveness of Positivstellensatz relaxation for stability analysis of polynomial fuzzy systems.

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