Distributed H∞ filter design for T-S fuzzy systems with Sigma-Delta quantisation via non-PDC scheme

The paper focuses on the distributed $ {H_\infty } $ H∞ filtering problem over wireless sensor networks (WSNs) for a class of discrete-time T-S fuzzy systems with immeasurable premise variables and Sigma-Delta $ (\sum \Delta ) $ (∑Δ) quantiser. Two defectives are considered including packet losses and multiplicative noises, which can be represented by some mutual independent random variables, respectively. Unlike conventional logarithmic quantiser, by utilising the Sigma-Delta dynamic quantiser, the quantised measurement outputs are broadcasted to the distributed filters over WSNs, only requiring a finite number of quantisation levels, and the static errors can be eliminated simultaneously. Using non-PDC scheme, an estimated premise variable-dependent distributed $ {H_\infty } $ H∞ filter is designed over WSNs. Then treating the premise variables as uncertainties, a robust distributed filtering problem is considered for such an uncertain filtering error system. Based on the fuzzy Lyapunov function, the less conservative mean-square stable conditions with a prescribed $ {H_\infty } $ H∞ performance index for the uncertain filtering error dynamical systems are presented. The filter parameters are determined by solving a set of linear matrix inequalities (LMIs). Finally, a tunnel diode circuit model and a numerical example are presented to illustrate the theoretical findings.