Relaxed Observer Design of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on a Lightweight Gain-Scheduling Law

This study is concerned with proposing much more effective Luenberger-like fuzzy observers than relevant multiinstant observers reported in recent literature, in other words, less conservative results can be given while less computing resource is consumed as an important premise. For the first time, the variation bound of two adjacent time-variant Lyapunov matrices encountered in the synthesis of fuzzy observer is characterized by a contraction factor, and thus the key replacement of the lagged term is developed in order to construct an effective synchronization framework of fuzzy observer synthesis. Since there only exist the current-time normalized fuzzy weighting functions in the obtained synchronization framework, the conservatism caused by the mismatch of different sampling instants can be avoided. Based on this, a lightweight gain-scheduling law is designed in which a large number of redundancy gains in recent multiinstant observers can be condensed in order to save computing resource to the greatest extent. Finally, two benchmark examples are borrowed for validating the superiority of our proposed results.