Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem

By Antonio Sala, C. Ariño. Fuzzy Sets Syst., 2007

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Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems (2008, methodology): “Moreover, the type-1 T-S fuzzy models employed in [4]–[10] are developed using type-1 fuzzy sets such that the grades of membership are certain.”
Fuzzy Control Systems: Past, Present and Future (2019, methodology): “Based on checking the positiveness of multidimensional matrices, the authors in [58] applied Pólya’s theorem to derive asymptotically necessary and sufﬁcient LMI-based conditions for the stability and performance of T-S fuzzy systems.”
Control Design for Interval Type-2 Fuzzy Systems Under Imperfect Premise Matching (2014, background): “More relaxed stability conditions under PDC can be found in [17]–[19].”
Robust Observer Design for Unknown Inputs Takagi–Sugeno Models (2013, methodology): “Another way to introduce relaxation is given by [16] using Polya’s theorem.”
Discrete‐time H − ∕ H ∞ sensor fault detection observer design for nonlinear systems with parameter uncertainty (2015, background): “Accordingly, the stability analysis of nonlinear T–S systems is simplified, where the derived conditions result are generally dependent on the choice of Lyapunov function [27].”