Dynamic Output Feedback-Predictive Control of a Takagi–Sugeno Model With Bounded Disturbance

This paper considers predictive control of a Takagi-Sugeno fuzzy model with bounded disturbance, strictly satisfying the input and state constraints. The membership-function-dependent dynamic output feedback law, as in a previous work, is utilized. The novelty lies in the following technical improvements. For the notion of quadratic boundedness, which specifies closed-loop stability and invariance properties, the full Lyapunov matrix is utilized. The real-time ellipsoidal bound of true state is recursively optimized by invoking the S-procedure. Some relaxation scalars, being optimized by the norm-bounding technique, are introduced for better handling the input and state constraints. The multistep approach, where a sequence of dynamic output feedback laws are optimized at each sampling instant, is given to improve the single-step approach. Numerical examples are given to illustrate the effectiveness of the proposed controllers.