Modified Looped Functional for Sampled-Data Control of T–S Fuzzy Markovian Jump Systems

Abstract

This article investigates the sampled-data control for a class of Takagi–Sugeno (T–S) fuzzy Markovian jump systems via a novel looped functional approach. By refining the fractional delayed state concept, the looped functional is established to include more sampling information of the intervals not only from <inline-formula><tex-math notation= LaTeX >$x(t_{k})$</tex-math></inline-formula> to <inline-formula><tex-math notation= LaTeX >$x(t)$</tex-math></inline-formula> but also from <inline-formula><tex-math notation= LaTeX >$x(t)$</tex-math></inline-formula> to <inline-formula><tex-math notation= LaTeX >$x(t_{k+1})$</tex-math></inline-formula>, which would contribute to a reduction in the conservatism. Then, a sufficient criterion is presented to ensure the stochastic stability of the resulting closed-loop system, based on which the sampled-data controller is further designed for the T–S fuzzy Markovian jump system under the influence of asynchronous premise variables. Finally, the obtained theorems are applied to a numerical example and a practical application to show the effectiveness and superiority of the proposed method.