Multi-Instant Gain-Scheduling Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on a Time-Variant Balanced Matrix Approach

This article is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and, thus, much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e., its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section.