Robust Admissible Analyse of Uncertain Singular Systems via Delta Operator Method.docVIP

Robust Admissible Analyse of Uncertain Singular Systems via Delta Operator Method 　　【Abstract】This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems（SDOSs）. Firstly, we introduce the definition of generalized quadratic admissibility to ensure robust admissibility. Then, by means of LMI, a necessary and sufficient condition is given to prove a uncertain SDOS is generalized quadratic admissible. Finally, a numerical example is provided to demonstrate the effectiveness of the results in this paper. 　　【Key words】SDOSs; Ｒobust admissibility; LMI 　　0　Introduction 　　Singular system was proposed in the 1970s[1]. It has irreplaceable advantages over normal system[2]. When normal system model describes practical system, it requires system is circular. There is output derivative existing in inverse system, and it causes normal system is not circular. Singular systems do not have this drawback. Any control systems have uncertain factor[3]. A delta operator method was presented in the 1980s by Goodwin and Middleton[4]. After that, we have obtained a lot of theoretical achievements.We can obtain delta operator as follows: 　　1　Preliminaries 　　These notations are put to use in this paper: Rn means n-dimensional real vector sets and Rm×n means m×n dimensional real matrix sets. The identity matrix with dimension r is denoted by Ir. Matrix Q＞0（or Q＜0） means that Q is positive and symmetric definite（or negative definite）. ?姿（E，A）={?姿∈Cdet（?姿E-A）=0}. The rank of a matrix A is denoted by rank（A）. Dint（b，r） is the interior of the region with the center at（b，0） and the radius equal to I in the complex plane. The shorthand diag（S1，S2...Sq） means the matrix is diagonal matrix with main diagonal matrix being the matrices S1，S2...Sq. 　　Considering the below SDOS described by： 　　E?啄x（tk）=A?啄x（tk）（１） 　　where tk means the time t＝kh. The sampling period h satisfy h＞0. x（tk）∈Rn is the state. E, A?啄∈Rn×n are known constant matrice