Relative Degrees and Adaptive Feedback Linearization Control of T–S Fuzzy Systems

This paper presents a new study on the relative degrees of single-input and single-output T-S fuzzy systems in general noncanonical forms, and proposes a feedback linearization-based control design method for such systems. The study extends the system relative degree concepts, commonly used for the control of nonlinear systems, to general T-S fuzzy systems, derives various relative degree conditions for general T-S fuzzy systems, and establishes the relative degree dependent normal forms. A feedback linearization-based control design framework is developed for general T-S fuzzy systems using its normal form, to achieve closed-loop stability and asymptotic output tracking under relaxed design conditions. A new adaptive feedback linearization-based control scheme for T-S fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed. Some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form T-S fuzzy systems are also demonstrated. An illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme.