Finite-Time Dynamic Event-Triggered Distributed $H_\infty$ Filtering for T-S Fuzzy Systems

Abstract

In this article, the problem of the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filtering in finite-time horizon is investigated for a class of Takagi–Sugeno (T-S) fuzzy systems with sensor saturation and unknown bounded noise. Considering the network bandwidth limitation, a dynamic event-triggered mechanism (ETM) is proposed. Due to an asynchronous problem of premise variables induced by the dynamic ETM, the partition approach is applied. Under the partition region, a novel piecewise T-S fuzzy distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filtering is derived. By constructing the Lyapunov function, sufficient conditions for the finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance of the estimation error system are given. Furthermore, to minimize the interference from disturbance to distributed filtering, the optimal problem of disturbance attenuate parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gamma$</tex-math></inline-formula> is solved. Finally, a simulation example is presented to verify the effectiveness of the proposed algorithm.