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

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Abstract
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.
Funding Information
  • National Natural Science Foundation of China (61374130)
  • Jiangsu Natural Science Foundation of China (SBK20130033)
  • Program for New Century Excellent Talents in the University of China (NCET-11-0830)

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