Robust } Filtering for a Class of Two-Dimensional Uncertain Fuzzy Systems With Randomly Occurring Mixed Delays

• Published in: IEEE transactions on fuzzy systems Vol. 25; no. 1; pp. 70 - 83
• Main Authors: Yuqiang Luo, Zidong Wang, Guoliang Wei, Alsaadi, Fuad E.
• Format: Journal Article
• Language: English
• Published: IEEE 01.02.2017
• Subjects: 2-D systems; Delays; Fornasini–Marchesini (FM) model; fuzzy basis function; Fuzzy systems; membership function; mixed time delays; parameter uncertainties; Robustness; spatial promise variable; Stochastic processes; Symmetric matrices; Takagi–Sugeno (T–S) fuzzy model; Uncertain systems; Uncertainty
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2016.2556001

This paper is concerned with the robust H ∞ filtering problem for a class of 2-D uncertain fuzzy systems with randomly occurring mixed delays (ROMDs). The underlying 2-D systems are described by the Fornasini-Marchesini model, and the uncertainty is expressed in a linear fraction form. An improved Takagi-Sugeno (T-S) fuzzy model corresponding to the spatial promise variables is adopted to represent the complicated 2-D nonlinear system. The mixed delays consisting of both discrete and distributed delays are allowed to appear in a random manner governed by two sets of Bernoulli distributed white sequences with known probability. A full-order fuzzy filter is constructed to estimate the output signal such that, in the presence of parameter uncertainties and ROMDs, the dynamics of the estimation errors is asymptotically stable with a prescribed H ∞ disturbance attenuation level. Based on the stochastic analysis technique and the Lyapunov-like functional, sufficient conditions are established to ensure the existence of the desired filters, and the explicit expressions of such filters are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages. A numerical example is provided to demonstrate the effectiveness of the developed filter design algorithms, and the filter performances with and without fuzzy rules are also compared.