Stabilization and set-point tracking for nonlinear discrete-time systems via feedback TS fuzzification

The stabilization and set-point tracking control problems are investigated for a class of nonlinear discrete-time systems via Takagi-Sugeno (TS) fuzzy control approach. The concept of feedback TS fuzzification is first introduced, which can be very conducive to conveniently transforming a general nonlinear system into a TS fuzzy model by coordinate transformation and feedback law. Then, a stabilizing controller for nonlinear discrete-time systems is proposed by using the feedback TS fuzzification and TS fuzzy control methods. And we provide a numerical example to show the effectiveness of feedback TS fuzzification. Finally, based on feedback TS fuzzification, we convert the set-point tracking problem of nonlinear discrete-time systems with immeasurable state variables into a stabilization problem of a tracking error system (a TS fuzzy model) by virtue of TS fuzzy observer-based control approach. Under some conditions, controller gains and observer gains can be designed separately by employing a delayed nonquadratic Lyapunov function. A practical example concerning mass-spring-damper systems demonstrates the efficiency of the set-point tracking control method.