Relative degrees and output tracking control of T-S fuzzy systems

This paper presents a new study on the relative degrees of T-S fuzzy systems: ẋ (t) = Σ_i=1^N μ_i(t)A_ix(t) + Σ_i=1^N μ_i(t)C_ix(t), where (A_i, B_i, C_i) are some non-canonical form matrices, and proposes a feedback linearization based control design method for such systems. The study extends the system relative degree concepts, commonly used for control of complex nonlinear systems, to T-S fuzzy systems, and derives various relative degree conditions for general T-S fuzzy systems and establishes the relative degree dependent normal forms. A feedback linearization control design procedure is developed for such a system using its normal form, to achieve closed-loop stability and output tracking under relaxed design conditions. An illustrative example is presented with simulation results to show the control system design procedure and desired performance.