【正文】 ntrol [M]. Englewood Cliffs, NJ: PrenticeHall, 1991 [13] Dong M and Gao Z W. H∞ faulttolerant control for singular bilinear systems related to output feedback[J]. Systems Engineering and Electronics, 2020, 28(12):18661869. (In Chinese) [14] Li T H S and Tsai S H. TS fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems [J]. IEEE Trans. Fuzzy Syst., 2020, 3(15):494505. [15] Tsai S H and Li T H S. Robust fuzzy control of a class of fuzzy bilinear systems with timedelay [J]. Chaos, Solitons and Fractals (2020), doi: . [16] Li T H S, Tsai S H, et al, Robust H∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems [J]. IEEE Trans. Syst., Man, and Cybe., 2020, 38(2) : 510526. 離散模糊雙線性系統(tǒng)的靜態(tài)輸出反饋控制 摘要 ：研究了一類離散模糊雙線性系統(tǒng) (DFBS)的靜態(tài)輸出反饋控制問(wèn)題。 linear matrix inequality (LMI) 1 Introduction It is well known that TS fuzzy model is an effective tool for control of nonlinear systems where the nonlinear model is approximated by a set of linear local models connected by IFTHEN rules. Based on TS model, a great number of results have been obtained on concerning analysis and controller design[1][11]. Most of the above results are designed based on either state feedback control or observerbased control[1][7].Very few results deal with fuzzy output feedback[8][11]. The scheme of static output feedback control is very important and must be used when the system states are not pletely available for feedback. The static output feedback control for fuzzy systems with timedelay was addressed [9][10] and a robust 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 controll