State Estimation of Discrete-Time Takagi–Sugeno Fuzzy Systems in a Network Environment

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 premise variables 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. It is assumed that the filter uses the most recent packet. If there are packet dropouts occurring, the filter adopts the information for the last received packet. Suppose that the mode of the Markov chain is ordered according to the number of consecutive packet dropouts from zero to a preknown maximal value. For each mode of the Markov chain, it only has at most two jumping actions: 1) jump to the first mode and the current packet is transmitted successfully and 2) jump to the next mode and the number of consecutive packet dropouts increases by one. 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.