Observer Design and H∞ Performance for Discrete-Time Uncertain Fuzzy-Logic Systems

The observer design and H
_∞
algorithm are proposed for the discrete-time fuzzy-logic systems in this article. The considered fuzzy-logic systems are subject to parameter uncertainty and unmeasurable state variables. To appropriately deal with parameter uncertainty and unmeasurable state variables, we first disintegrate the space of premise variables, then the total partitioned regions will be divided into two kinds: 1) crisp regions and 2) fuzzy regions. With the aid of partitioned regions, piecewise fuzzy H
_∞
observers are presented. Availability of the piecewise fuzzy H
_∞
observers gives us an accurate picture of the overall evolution of the augmented systems leading therefore to an improved situational awareness for the noncoordination of premise variables and external interference and, hence, the augmented systems achieve the performance conditions: asymptotic convergence and H
_∞
performance. The simulation results of the proposed approach show the accuracy of the resulting state estimates.