Equivalent techniques, extra comparisons and less conservative control design for Takagi–Sugeno (TS) fuzzy systems

Abstract

This study is divided in three parts. In the first part, the equivalence of recent strategies for stability analysis, namely the null term, the Finsler's lemma and the descriptor approach is demonstrated in the context of fuzzy Lyapunov functions (FLFs). In the sequel, this study presents new insights concerning the extension of typical right-hand side relaxations and the use of the FLF structure. Finally, an alternative less conservative non-parallel distributed compensation control design is proposed that generalises previous approaches.