Relaxed, dissipative fuzzy control - Polya theorem

• Main Authors: Jia-ren Wan, 萬嘉仁
• Other Authors: Ji-chang Lo
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/39353755319459752302

碩士 === 國立中央大學 === 機械工程研究所 === 96 === In this thesis, we propose a general quadratic dissipative state feedback control method to solve a stabilization problem for fuzzy system with sector-bounded type nonlinearities at the input. The problem covers the bounded real, positive real and sector-bounded performance as a special case by choosing the corresponding quadratic supply rate. Moreover, we also prove necessary and sufficient conditions to state feedback controllers ensuring quadratic stability for Takagi-Sugeno fuzzy systems in theory. But our main objective is to generate a family of linear matrix inequalities based on an extension of Polya theorem (a.k.a. Matrix-valued Polya theorem). The proposed conditions are stated as progressively less conservative sets of linear matrix inequalities, allowing us to obtain a solution for the quadratic stabilizability problem whenever a solution exists. At last, an additional relaxed condition is also provided, relying on the use of slack matrix variables. All proposed methods will be shown via theoretical analysis and numerical simulations.