H\infty Control for 2-D Fuzzy Systems With Interval Time-Varying Delays and Missing Measurements

• Published in: IEEE transactions on cybernetics Vol. 47; no. 2; pp. 365 - 377
• Main Authors: Yuqiang Luo, Zidong Wang, Jinling Liang, Guoliang Wei, Alsaadi, Fuad E.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 2-D systems; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <inline-formula> <tex-math notation="LaTeX"> H_\infty </tex-math> </inline-formula> control; Computer simulation; Control systems; Control systems design; Convexity; Delays; Feedback control; Fuzzy control; Fuzzy systems; H-infinity control; missing measurements; Nonlinear systems; Optimization; Output feedback; Performance indices; State space models; Stochastic processes; Symmetric matrices; Time varying control systems; time-varying delays; Time-varying systems; Two dimensional models
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2016.2514846

In this paper, we consider the H ∞ control problem for a class of 2-D Takagi-Sugeno fuzzy described by the second Fornasini-Machesini local state-space model with time delays and missing measurements. The state delays are allowed to be time-varying within a known interval. The measurement output is subject to randomly intermittent packet dropouts governed by a random sequence satisfying the Bernoulli distribution. The purpose of the addressed problem is to design an output feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H ∞ performance index is satisfied. By employing a combination of the intensive stochastic analysis and the free weighting matrix method, several delay-range-dependent sufficient conditions are presented that guarantee the existence of the desired controllers for all possible time-delays and missing measurements. The explicit expressions of such controllers are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.