Feedback-linearization-based control of discrete-time quadratic TS fuzzy systems with disturbances

Controlling a dynamic system to make its output identical to a user-desired reference trajectory given to the system's input without any delay (i.e., perfect output tracking control) is an important and frequently encountered control requirement in industries (e.g., robotic control). When disturbances exist in a system, perfect output tracking control may be impossible to attain and alternatively asymptotical output tracking is sought. This paper presents an asymptotical output tracking control design method for a general class of discrete-time TS fuzzy systems with quadratic rule consequents, which offer better modeling capabilities than the linear rule consequents. The control problem is dealt with by utilizing the feedback linearization method. To guarantee asymptotical output tracking performance in the presence of square disturbance signal, an auxiliary PI controller is added to attenuate the disturbance. The feedback linearization method is known in the literature to fail to work for certain systems because it can make the tracking controller's output unbounded. To address this issue, we put forward a full block S-procedure condition to check whether such failure will occur for any given quadratic TS fuzzy system. Applying feedback linearization to the quadratic TS fuzzy systems is innovative relative to the literature that has exclusively dealt with the TS fuzzy systems with linear rule consequents only. Two numerical examples are provided to illustrate the effectiveness and utility of our theoretical results.