Average consensus with weighting matrix design for quantized communication on directed switching graphs

We study average consensus for directed graphs with quantized communication under fixed and switching topologies. In the presence of quantization errors, conventional consensus algorithms fail to converge and may suffer from an unbounded asymptotic mean square error. We develop robust consensus algorithms to reduce the effect of quantization. Specifically, we introduce a robust weighting matrix design and use the H1 performance index to measure the sensitivity from the quantization error to the consensus deviation. Linear matrix inequalities are used as design tools. The mean square deviation is proven to converge and its upper bound is explicitly given in the case of fixed topology with probabilistic quantization. Numerical results demonstrate the effectiveness of this method. Copyright © 2012 John Wiley & Sons, Ltd.