Simultaneous Estimation of State and Unknown Input for TS Fuzzy Systems with Unmeasured Premise Variables

Designing unknown input (UI) observers for Takagi-Sugeno (TS) fuzzy systems is known as a challenging issue, especially when the premise variables are unmeasured. This paper presents a new approach to deal with unmeasured premise variables in UI observer design for discrete-time TS fuzzy systems. With an effective reformulation of nonlinear systems, the unmeasured nonlinearities are regarded as local nonlinear consequent parts of the fuzzy systems. The differential mean value theorem is applied to transform the mismatch terms caused by unmeasured premise variables into a convex representations efficiently. In contrast to the existing methods for observer synthesis, a relatively simple solution to UI observer design can be obtained based on fewer fuzzy rules and less computational burden. Simulation example is given to demonstrate the validity and applicability of the proposed approach.