Quantized insensitive consensus of Lipschitz nonlinear multi-agent systems using the incidence matrix

Abstract

This paper concerns the quantization effect on an insensitive control law for Lipschitz nonlinear multi-agent systems with quantization information under undirect communication graphs. Quantized insensitive consensus control laws are implementable with quantized values of the relative states by using incidence matrix instead of adjacency matrix. The designed controllers are insensitive to additive interval-bounded controller coefficient variations, where a new technique by converting interval-bounded variation format to norm-bounded uncertain format is proposed to solve numerical problem caused by interval-bounded variations effectively. By taking advantage of tools from non-smooth analysis, explicit convergence results are derived for both uniform and logarithmic quantizers with the aid of linear matrix inequality (LMI) technique. It is pointed out that finite time practical consensus can be achieved when uniform quantizers are used, while consensus can be achieved under some conditions when a logarithmic quantizer is considered. Sufficient conditions of the existence of the proposed control strategy are also obtained by using matrix inequality technique. Simulation example is provided to illustrate the results.