Set-Membership Observer Design for T-S Fuzzy 2-D Systems With Unmeasurable Premise Variables

In this article, a set-membership estimation observer is designed for Takagi–Sugeno (T-S) fuzzy 2-D systems on Roesser model. The T-S fuzzy 2-D systems have unmeasurable premise variables, which cause prescribed influence to estimation. First, the observer and error systems are built and analyzed based on parallel distributed compensation. Then, the observer gain matrices are computed by solving an optimal problem to ensure the radius of error zonotopes converge to zero, so that estimation errors are asymptotically stable. In addition, we prove that the radius of error zonotope satisfies
$L_\infty$
performance. To demonstrate the effectiveness of proposed method, a T-S fuzzy 2-D system transformed from a nonlinear Darboux equation is studied and the simulation results are presented to show the advantage of proposed approach.