Yang Wang, Yiyong Yang, and Fuchun Sun
Fuzzy system, singular perturbation, actuator saturation, deltaoperator
The robust controller performances of singularly perturbation system could not satisfy the needs of industrial application, because of the perturbation parameters and the problem of crowding poles within the boundary of stability circle at high sampling frequency by traditional shift operator. This paper adopt delta operator instead of traditional shift operator solving the problem of crowding poles at high sampling frequency. The Takagi-Sugeno (TS) fuzzy singularly perturbation model is employed to design the robust controller of the continuous-time systems with actuator saturation, where the continuous-time singularly perturbation model is described by delta operator. Then, the parallel distributed compensation is used to design the controller, and then the system stability is proved with the Lyapunov function. Moreover, a set invariance condition is given for TS fuzzy singularly perturbation delta operator system, and then the ellipsoid and polyhedron contractive invariant conditions are derived with the help of the auxiliary feedback matrix by optimization. At last, numerical examples are given to illustrate the effectiveness of the designed controller.
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