A novel Takagi-Sugeno fuzzy observer using periodic memory sampled-data for Takagi-Sugeno fuzzy time-delay model and its application to the stirred tank reactor nonlinear time-delay system

In this paper, we propose the design of Takagi-Sugeno (T-S) fuzzy observers using periodic memory sampled-data for T-S fuzzy time-delay models with disturbances in the state and output vectors. For the first time, a novel structure of T-S fuzzy observers for the T-S fuzzy time-delay models is proposed, where the information of the output and delayed-output vectors is sampled at discrete time instants. Existence conditions for the proposed T-S fuzzy observer are established and formulated in terms of a convex optimisation problem, which provides unknown observer matrices and minimises the error in estimation. An effective algorithm is provided to design the proposed T-S fuzzy observers. The obtained theoretical results are applied to estimate the state vector of the stirred tank reactor nonlinear time-delay system.