On the designing of robust dynamic observers for continuous-time systems in T-S fuzzy model with interval time-varying delays

Abstract

Delay-dependent robust [Formula: see text] fuzzy dynamic observers (HFDOs) for continuous-time T-S fuzzy systems with interval time-varying delays, are studied here, considering the presence of exogenous disturbances. The proposed approach involves the creation of an augmented Lyapunov-Krasovskii functional through the utilization of an integral inequality based on the Wirtinger-based integral inequality and the extended reciprocally convex combination inequality. These techniques lead to delay-dependent conditions that are less conservative and that can be represented as a set of linear matrix inequalities, solvable using the YALMIP toolbox. Two detailed examples are presented at the end of the paper to illustrate the overall effectiveness of the proposed observer, which performs better than existing observers such as the [Formula: see text] fuzzy proportional observer (HFPO) and the [Formula: see text] fuzzy proportional-integral observer (HFPIO).