Impulse Elimination of the Takagi–Sugeno Fuzzy Singular System Via Sliding-Mode Control
Yi Zhang, Zhenghong Jin, Qingling Zhang
Abstract
The problems of impulse controllability and impulse elimination are investigated based on sliding-mode control (SMC) for Takagi–Sugeno (T–S) fuzzy singular systems (FSSs) in this article. Necessary and sufficient conditions for T–S FSSs to be impulse controllable are obtained based on the rank of matrices of system equivalent form. The relationship between impulses and fuzzy membership functions is given. The linear switching function and SMC law are designed to be applied to the impulse elimination of T–S FSSs. The main contributions of this approach are to design an SMC law, which can not only effectively eliminate impulses of T–S FSSs but also make the system asymptotically stable and give the principle of SMC to eliminate the impulse. Finally, the proposed method is applied to three examples. Examples 1 and 3 are to illustrate that SMC can effectively eliminate impulses of T–S FSSs. Example 2 verifies the superiority of this method by comparing with proportional and derivative feedback control law.