Fuzzy gain scheduling: controller and observer design based on Lyapunov method and convex optimization

This paper addresses model-based fuzzy control. A constructive and automated method for the design of a gain-scheduling controller is presented. Based on a given Takagi–Sugeno fuzzy model of the plant, the controller is designed such that stability and prescribed performance of the closed loop are guaranteed. These properties are valid in a wide working range around an equilibrium without restrictions to slowly varying trajectories. The synthesis is based on linear matrix inequalities and convex optimization techniques. If required, a fuzzy state estimator and an extended controller can be included, providing a zero steady-state error in the presence of disturbances and modeling errors. The proposed method has been applied to a control of a laboratory liquid-level process. Hence, the performance has been evaluated in simulations as well as in real-time control.