stability analysis of fuzzy Polynomial fractional differential Systems using Sum-of-Squares

This paper discusses the stability analysis of fractional-order polynomial systems by using the sum of squares method. furthermore the feasibility of designing the problems demonstrates which can not be represented in LMIs. unlike the T-S fuzzy model which can only work with fixed matrices, this method deal with polynomial matrices. Therefore, displaying a nonlinear system model using polynomials is a more efficient way. The stabilization of fractional order systems based on the fuzzy T-S model is expressed according to Lyapunov theory of stability by linear matrix inequality (LMI) while stability analysis polynomial fuzzy is based on the sum of the square. The main advantage of the method is the stabilization of fractional order systems based on the fuzzy T-S model. the stabilization conditions are expressed according to Lyapunov theory of stability by linear matrix inequality (LMI) while stability analysis is based on the polynomial fuzzy model. the systems where LMI optimization methods do not work, stability analysis and controller design can be performed by SOSTOOLS. In this paper, the stability conditions of a fractional-order polynomial fuzzy system are investigated then obtained necessary and sufficient conditions for stability. Finally, shown an example of the accuracy and The correctness of the proposed method.