Adaptive Control of Discrete-Time T-S Fuzzy Systems with Multiple Input-Output Delays

This paper derives a new prediction model of global discrete-time input-output multiple-delay Takagi-Sugeno (T-S) fuzzy systems with multiple delays and employs it for adaptive fuzzy control in the presence of system parameter uncertainties. Based on a model-based approach, a new system parametrization and adaptive control scheme are developed with detailed design procedure and complete stability analysis. The derived new fuzzy prediction model involves not only the current values of the membership functions but also their past values, expanding its capacity of approximating dynamic systems. A stable adaptive law is developed based on an error model resulted from a new augmented parametric model for which a signal bounding property is also proved, crucial for closed-loop system stability. An illustrative example is presented to demonstrate the studied new concepts and to verify the desired performance of the new types of adaptive fuzzy control systems.