Multiple Delay-Dependent Robust $H_\infty$ Finite-Time Filtering for Uncertain Itô Stochastic Takagi–Sugeno Fuzzy Semi-Markovian Jump Systems With State Constraints

This article investigates multiple delay-dependent robust
$H_\infty$
finite-time filtering for uncertain Itô stochastic Takagi–Sugeno (T–S) fuzzy semi-Markovian jump systems with state constraints. Few studies exist for Itô stochastic T–S fuzzy semi-Markovian jump systems with state constraints. First, a T–S fuzzy semi-Markovian jump filter is explored and a controller is designed. In terms of linear matrix inequalities, delay-dependent sufficient conditions as well as bounded real lemma are gathered by utilizing stochastic Lyapunov function. Robust finite-time boundedness and input–output finite-time mean square stabilization are achieved and gain matrices of the filter and controller are obtained at the same time. A numerical example is presented to validate the feasibility of the proposed results in this article. And the admissible maximal delay bounds are calculated.