Robust normalization and H∞ stabilization for uncertain Takagi-Sugeno fuzzy singular systems with time-delays

Abstract

Abstract This work deals with the simultaneous robust normalization and H∞ stabilization problems for uncertain Takagi-Sugeno fuzzy singular systems (TSFSSs) with time-delays via a novel fuzzy proportional-derivative state feedback controller (PDSFC). It is worth pointing out that the uncertainties involved in this paper exist in all different system matrices including Ei. Without using any model transformations, some new criteria that ensure the closed-loop system to be robustly normal and stable for all admissible uncertainties are exactly deduced by means of the free-weighting matrix method, and clearly expressed as strict linear matrix inequalities. Meanwhile, the prescribed H∞ performance is also achieved. Then, based on the obtained criteria, the specific expression of desired fuzzy PDSFC is given. Finally, the correctness and feasibility of our theoretical results are verified via two academic examples.