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

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.