【正文】 H∞ controller via static output feedback was designed[11]. But the derived conditions are not solvable by the convex programming technique since they are bilinear matrix inequality problems. Moreover, it is noted that all of the aforementioned fuzzy systems were based on the TS fuzzy model with linear rule consequence. Bilinear systems exist between nonlinear and linear systems, which provide much better approximation of the original nonlinear systems than the linear systems [12].The research of bilinear systems has been paid a lot of attention and a series of results have been obtained[12][13].Considering the advantages of bilinear systems and fuzzy control, the fuzzy bilinear system (FBS) based on the TS fuzzy model with bilinear rule consequence was attracted the interest of researchers[14][16]. The paper [14] studied the robust stabilization for the FBS, then the result was extended to the FBS with timedelay[15]. The problem of robust stabilization for discretetime FBS (DFBS) was considered[16]. But all the above results are obtained via state feedback controller. In this paper, a new approach for designing a fuzzy static output feedback controller for the DFBS is proposed. Some sufficient conditions for synthesis of fuzzy static output feedback controller are derived in terms of linear matrix inequality (LMI) and the controller can be obtained by solving a set of LMIs. In parison with the existing literatures, the drawbacks such as coordinate transformation and same output matrices have been eliminated. Notation: In this paper, a real symmetric matrix 0P? denotes P being a positive definite matrix. In symmetric block matrices, an asterisk (*) is used to represent a symmetric term and {...}diag stands for a blockdiagonal matrix. The notion , , 1si jl?? means 1 1 1s s si j l? ? ?? ? ? . 2 Problem formulations Consider a DFBS that is represented by TS fuzzy bilinear model. The i th rule of the DFBS is represented by the following form 11 ( ) .. . ( ) ( 1 ) ( ) ( ) ( ) ( )( ) ( ) 1 , 2 ,.. .,ii v v ii i iiR if t is M an d an d t is Mthe n x t A x t B u t N x t u ty t C x t i s??? ? ? ??? (1) Where iR denotes the fuzzy inference rule, s is the number of fuzzy rules. , 1,2...jiM j v? is fuzzy set and ()j t? is premise variable. () nxt R? Is the state vector, ()ut R? is the control input and T12( ) [ ( ) , ( ) , .. , ( ) ] qqy t y t y t y t R?? is the system output. The matrices , , ,i i i iA B N C are known matrices with appropriate dimensions. Since the static output feedback control is considered in this paper, we simply setvq? and 11( ) ( ) , ..., ( ) ( )vqt y t t y t????. By using singleton fuzzifier, product inference and centeraverage defuzzifier, the fuzzy model (1) Can be expressed by the following global model 11( 1 ) ( ( ) ) [ ( ) ( ) ( ) ( ) ]( ) ( ( ) ) ( )si i i iisiiix t h y t A x t B u t N x t u ty t h y t C x t??? ? ? ???? (2)Where 1 1( ( ) ) ( ( ) ) / ( ( ) ) , ( ( ) ) ( ( ) )qsi i i i iji jh y t y t y t y t y t? ? ? ?? ???? ?. ( ( ))ij yt? is the grade of Membership of ()jyt in jiM . We assume that ( ( )) 0i yt? ? and 1 ( ( )) 0s ii yt?? ?? . Then we have the following conditions: 1( ( ) ) 0 , ( ( ) ) 1siiih y t h y t???? .Based on parallel distribute pensation, the fuzzy controller shares the same premise parts with (1)。最后，通過仿真例子驗(yàn)證了方法的有效性。文 [5][6]研究了模糊時(shí)滯系統(tǒng)的靜態(tài)輸出反饋控制問題，文 [8]第一次提出了模糊靜態(tài)輸出反饋 H∞ 控制的問題。考慮 TS 模型的有效性及雙線性系統(tǒng)的特點(diǎn)，對(duì) TS 模糊雙線性系統(tǒng)（ FBS）的研究引起了很多學(xué)者的關(guān)注 [14][15]。 綜上分析，本文研究了一類用 TS模型表示的 DFBS靜態(tài)輸出反饋控制問題。 注 1：在本文中， nR 表示 n 維 Euclidean 空間， 0( 0)PP??表示是一個(gè)正定（正半定）實(shí)對(duì)稱矩陣。 1 系統(tǒng)的模型描述 由 TS模型描述的不確定模糊雙線性系統(tǒng) ,它的第 i 條規(guī)則可描述如下 : 11 ( ) .. . ( ) ( 1 ) ( ) ( ) ( ) ( )( ) ( ) : { 1 , 2. .. .. }i i ivvi i iiR if t is M an d an d t is Mthe n x t A x t B u t N x t u ty t C x t i I s??? ? ? ?? ? ? （ 1）其中：ijF 是模糊集合， 1,2,...,jv? ， 12( ) [ ( ) , ( ) .. . ( ) ]Tvt t t t? ? ? ?? 是前提變量 。 通過單點(diǎn)模糊化，乘積推理和中心平均反模糊化方法，模糊控制系統(tǒng)的總體模型為： 11( 1 ) ( ( ) ) [ ( ) ( ) ( ) ( ) ]( ) ( ( ) ) ( )si i i iisiiix t h y t A x t B u t N x t u ty t h y t C x t??? ? ? ???? （ 2） 其中： 11( ( ) )( ( ) ) , ( ( ) ) ( ( ) )( ( ) ) vii i ijsjiiyth y t y t y tyt? ??????? ?? 。以下在不引起混淆的情況下記 ( ())ih yt為 ih 。 （ 6 證明：考慮： 1 1 1 12 2 2 2( ) ( ) ( ) ( )T T T TM P N N P M P M P N P N P M? ? ? 由文 [1]中引理 1： 1T T T TM N N M M M N N?? ?? ? ?，可得到： 1T T T TM PN N PM M PM N PN?? ?? ? ?。 沿著系統(tǒng)（ 5）的軌線，對(duì) ()Vt求差分，可得到： , , 1 , , 112, , 1 , , 1( ) ( 1 ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )TTss T T Ti j l m n p ij l m n pi j l m n pss T T T Ti j l m n p ij l m n p ij l m n pi j l m n pV t x t P x t x t P x th h h h h h x t P x t x t P x th h h h h h x t P P x t x t P x t????? ? ? ? ?? ? ? ?? ? ? ? ? ? ?????（ 9）由引理 1 可知： T T T T