Time-varying output-based Takagi–Sugeno fuzzy controller of uncertain nonlinear systems

This paper proves the ultimately boundedness analysis for the trajectory tracking problem between the states of an uncertain nonlinear system represented by a Takagi–Sugeno (T–S) system and a given set of desired trajectories. The design of an output feedback controller includes a weighted contribution of the models included in the T–S design. The proposed T–S fuzzy estimates the state variables based on the output information, exclusively. The output-based controller design uses a time-dependent Lyapunov function yielding the characterisation of ultimate boundedness for the trajectory tracking error. Sufficient conditions are obtained to ensure the existence of positive-definite solutions for two coupled time-varying matrix Riccati equations, which are needed to solve the tracking problem. A simplified scheme determines the gains for the feedback controller and observer. The proposed control law solves the trajectory tracking of an autonomous underwater vehicle. In this case, numerical solutions show that the controller forced the convergence of the tracking error after 2.0 seconds. An alternative control design approach based on linear matrix inequalities (LMI) is used for comparison purposes. The suggested controller forces a faster convergence of the tracking error than the LMI-based one and provides a smaller ultimate bound.