Robust ℋ∞ filtering of discrete-time networked nonlinear systems approximated by Takagi-Sugeno fuzzy technique

In this paper, we investigate the ℋ_∞ filtering problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems in a network environment. Different from the well used assumption that the normalized fuzzy weighting function for each subsystem is available at the filter node, we consider a practical case in which not only the measurement but also the normalized fuzzy weighting functions are transmitted via the network medium to the filter node. For the network characteristics, we consider the multiple packet dropouts which are described by using a Markov chain.We aim to design mode-dependent and fuzzy-basis-dependent T-S fuzzy filter by using the transmitted packet subject to the described network issue. With the augmentation technique, we obtain a stochastic filtering error system in which the filter parameters and the Markovian jumping variable are all involved. A sufficient condition which guarantees the stochastic stability and the ℋ_∞ performance is derived with the Lyapunov method. Based on the sufficient condition, we propose the filter design method and the filter parameters can be determined by solving a set of linear matrix inequalities (LMIs). A tunnel-diode circuit in a network environment is presented to show the effectiveness and the advantage of the proposed design approach.