On the Crucial Role of Antecedent-Consequent Structure Selection in LMI-Based PDC Control of TS Fuzzy Systems

Abstract

This paper demonstrates that how the selection of antecedent–consequent structures in a TS fuzzy model plays a crucial role in the feasibility, conservativeness and optimality of Linear Matrix Inequality (LMI)-based Parallel Distributed Compensation (PDC) fuzzy control design. Specifically, the paper provides the first formal theoretical and necessity proofs that the resulting controller cannot be regarded as definitive or optimal until it is ensured that the best possible antecedent–consequent structure has been identified. The paper further proves that this sensitivity to the selection of the antecedent–consequent structure is an inherent and highly influential property of all qLPV systems. The practical implication of these results is that, systematically exploring antecedent–consequent structures may considerably improve the resulting control performance. This paper does not directly propose a new control design method. Instead, the mathematical framework developed in the proofs may serve as a first-order solution and as a foundation for future research on antecedent–consequent structure exploration strategies. To support the theoretical results, a comprehensive analysis of conceptual examples is presented that is well suited for geometric visualization and highlights the general occurrence and practical significance of the problem. In addition, a dynamically complex real-world engineering benchmark example is examined, demonstrating how exploring the antecedent–consequent structures leads to better solutions than those previously published.