This paper investigates a fuzzy model reference adaptive controller (FMRAC) for continuous-time multiple-input-multiple-output (MIMO) nonlinear systems. The proposed adaptive scheme uses a Takagi-Seguno (TS) fuzzy adaptive system, which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators (e.g., state feedback) for those operating points. A proportional-integral update law is used to obtain a fast parameters adaptation. Stability and robustness of this adaptive scheme are established using Lyapunov stability tools. The simulation results, for a two-link robot, confirm the performance of the proposed approach.
In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.
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