Tham khảo tài liệu 'systems, structure and control 2012 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Enhanced Fuzzy Controller for Nonlinear Systems Membership-Function-Dependent Stability Analysis Approach 153 V t x t T Px t x t T Px t X T ppp Ị i 222 mm Ai BiGjk x t I Px t i 1 j 1 k 1 J f PPP X x t T pI 222 wmjmk Ai BiGjk x t Ỳi 1 j 1 k 1 ppp il Vr ú 222 mm. x t Ai BiGjk T P p a B Gjk x t i 1 j 1 k 1 ppp - t 222 z t T x Ai BiGjk T a Bi G jk x z t 12 i 1 j 1 k 1 where z t X-1x t and X P-1 e 3Ĩ Z . Let G jk N jk X1 where N jk e R m . From 12 we have p p p V t 2 2 2 Wimjmkz t T ijkz t 13 where ijk AiX XAi T Bi N jk NjkT Bi T . To facilitate the stability analysis the membership functions of the fuzzy controllers are designed as follows. w Wi- pm ơt 0 i 1 2 . p 14 where p and ơi are scalars to be determined. From 12 we have ppp V t 2 ỊL 2 w Pimi ơi - Pimi ơi mjmkz t T ijkz t z t 15 ppp 222 mtmjmkz t T Pi ijkz t 222mjmkz t T ơ ijkz t i 1 j 1 k 1 i 1 j 1 k 1 ppp 222wimjmkz t T ijkz t i 1 j 1 k 1 f p 222mmm z t TI pAk 2 ijk i 1 j 1 k 1 Ỳ l 1 ppp 222wmjmkz t T ijkz t i 1 j 1 k 1 To alleviate the conservativeness of the stability analysis from 14 we consider the following conditions. wi- Pimi i - 7imi Zi wi- Yimi Zi 0 i 1 2 . p 16 154 Systems Structure and Control where Y and Zi are scalars to be determined. The membership function conditions of 14 and 16 offer the condition to guide the design of the membership functions of fuzzy controller. Under these conditions some free matrices can be introduced to relax the conservativeness of stability analysis due to the imperfect match of membership functions. From 16 we consider the following condition to introduce some free matrices to 15 . -22 2 j - Yjmj Z m sijk sijk 0 17 where Sjk sjikT e 3Ĩ Z and Sjk sijkT 0 j k 1 2 . p i j. Furthermore considering p the property of the membership functions in 3 and 8 we have 2 - m 0 which leads ppp to 2 2 2 i - mị mjmk Vj Vjk 0 for arbitrary matrix of Vjk elỉ . From 15 and 17 i 1 j 1 k 1 we have k. k. k. C p A V t 222mm t p - 2ơi bk z t i 1 j 1 k 1 V l 1 j ppp ppp 222 imjmkz t ijkz t
