Unknown Input Functional Observer Design for Discrete-Time Interval Type-2 Takagi–Sugeno Fuzzy Systems

• Published in: IEEE transactions on fuzzy systems Vol. 30; no. 11; pp. 4690 - 4701
• Main Authors: Li, Yueyang, Yuan, Ming, Chadli, Mohammed, Wang, Zi-Peng, Zhao, Dong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Discrete time; Fuzzy systems; interval type-2 Takagi–Sugeno (T-S) fuzzy systems; Loss measurement; Mathematical models; Matrices (mathematics); matrix equation; Observers; State estimation; State observers; State vectors; Symmetric matrices; Takagi-Sugeno model; Uncertainty; unknown input observer (UIO); unmeasurable premise variables
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3156735

This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi-Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.